diff --git a/src/cdsat/TVar.ml b/src/cdsat/TVar.ml
index a67c08d2..2629f108 100644
--- a/src/cdsat/TVar.ml
+++ b/src/cdsat/TVar.ml
@@ -25,9 +25,8 @@ type store = {
   value: Value.t option Vec.t;
   reason: reason Vec.t;
   theory_views: theory_view Vec.t;
-  watches: t Vec.t Vec.t;
   has_value: Bitvec.t;
-  new_vars: Vec_of.t;
+  new_vars: Vec_of.t; (* TODO: a recycle vec to reuse identifiers *)
 }
 
 (* create a new variable *)
@@ -39,7 +38,6 @@ let new_var_ (self : store) ~term:(term_for_v : Term.t) ~theory_view () : t =
     term;
     level;
     value;
-    watches;
     reason;
     theory_views;
     has_value;
@@ -52,7 +50,6 @@ let new_var_ (self : store) ~term:(term_for_v : Term.t) ~theory_view () : t =
   Vec.push value None;
   (* fake *)
   Vec.push reason dummy_reason_;
-  Vec.push watches (Vec.create ());
   Vec.push theory_views theory_view;
   Bitvec.ensure_size has_value (v + 1);
   Bitvec.set has_value v false;
@@ -65,6 +62,9 @@ let[@inline] get_of_term (self : store) (t : Term.t) : t option =
 let[@inline] has_value (self : store) (v : t) : bool =
   Bitvec.get self.has_value v
 
+let[@inline] equal (a : t) (b : t) = a = b
+let[@inline] compare (a : t) (b : t) = compare a b
+let[@inline] hash (a : t) = CCHash.int a
 let[@inline] level (self : store) (v : t) : int = Veci.get self.level v
 let[@inline] value (self : store) (v : t) : _ option = Vec.get self.value v
 let[@inline] theory_view (self : store) (v : t) = Vec.get self.theory_views v
@@ -77,10 +77,6 @@ let[@inline] bool_value (self : store) (v : t) : _ option =
 
 let[@inline] term (self : store) (v : t) : Term.t = Vec.get self.term v
 let[@inline] reason (self : store) (v : t) : reason = Vec.get self.reason v
-let[@inline] watchers (self : store) (v : t) : t Vec.t = Vec.get self.watches v
-
-let[@inline] add_watcher (self : store) (v : t) ~watcher : unit =
-  Vec.push (watchers self v) watcher
 
 let assign (self : store) (v : t) ~value ~level ~reason : unit =
   Log.debugf 50 (fun k ->
@@ -115,7 +111,6 @@ module Store = struct
       reason = Vec.create ();
       term = Vec.create ();
       level = Veci.create ();
-      watches = Vec.create ();
       value = Vec.create ();
       theory_views = Vec.create ();
       has_value = Bitvec.create ();
@@ -133,6 +128,28 @@ module Tbl = Util.Int_tbl
 module Set = Util.Int_set
 module Map = Util.Int_map
 
+module Dense_map (Elt : sig
+  type t
+
+  val create : unit -> t
+end) =
+struct
+  type elt = Elt.t
+  type t = { v: elt Vec.t } [@@unboxed]
+
+  let create () : t = { v = Vec.create () }
+
+  let[@inline] get self v =
+    Vec.ensure_size_with self.v Elt.create (v + 1);
+    Vec.get self.v v
+
+  let[@inline] set self v x =
+    Vec.ensure_size_with self.v Elt.create (v + 1);
+    Vec.set self.v v x
+
+  let[@inline] iter self ~f = Vec.iteri self.v ~f
+end
+
 module Internal = struct
   let create (self : store) (t : Term.t) ~theory_view : t =
     assert (not @@ Term.Weak_map.mem self.of_term t);
diff --git a/src/cdsat/TVar.mli b/src/cdsat/TVar.mli
index b16235b3..9e46e27b 100644
--- a/src/cdsat/TVar.mli
+++ b/src/cdsat/TVar.mli
@@ -23,6 +23,8 @@ end
 module Vec_of : Vec_sig.S with type elt := t
 (** Vector of variables *)
 
+include Sidekick_sigs.EQ_ORD_HASH with type t := t
+
 type store = Store.t
 
 type reason =
@@ -53,13 +55,6 @@ val theory_view : store -> t -> theory_view
 val assign : store -> t -> value:Value.t -> level:int -> reason:reason -> unit
 val unassign : store -> t -> unit
 
-val watchers : store -> t -> t Vec.t
-(** [watchers store t] is a vector of other variables watching [t],
-    generally updated via {!Watch1} and {!Watch2}.
-    These other variables are notified when [t] is assigned. *)
-
-val add_watcher : store -> t -> watcher:t -> unit
-
 val pop_new_var : store -> t option
 (** Pop a new variable if any, or return [None] *)
 
@@ -69,6 +64,23 @@ module Tbl : CCHashtbl.S with type key = t
 module Set : CCSet.S with type elt = t
 module Map : CCMap.S with type key = t
 
+(** A map optimized for dense storage.
+
+  This is useful when most variables have an entry in the map. *)
+module Dense_map (Elt : sig
+  type t
+
+  val create : unit -> t
+end) : sig
+  type elt = Elt.t
+  type t
+
+  val create : unit -> t
+  val get : t -> var -> elt
+  val set : t -> var -> elt -> unit
+  val iter : t -> f:(var -> elt -> unit) -> unit
+end
+
 (**/**)
 
 module Internal : sig
diff --git a/src/cdsat/core.ml b/src/cdsat/core.ml
index ae32acbd..ee85f22d 100644
--- a/src/cdsat/core.ml
+++ b/src/cdsat/core.ml
@@ -19,6 +19,19 @@ type pending_assignment = {
   reason: Reason.t;
 }
 
+type plugin_id = int
+(** Each plugin gets a unique identifier *)
+
+type plugin_event = ..
+
+type watch_request =
+  | Watch2 of TVar.t array * plugin_event
+  | Watch1 of TVar.t array * plugin_event
+
+module Watches = Watch_schemes.Make (struct
+  type t = plugin_id * plugin_event
+end)
+
 type t = {
   tst: Term.store;
   vst: TVar.store;
@@ -29,6 +42,7 @@ type t = {
   term_to_var: Term_to_var.t;
   vars_to_decide: Vars_to_decide.t;
   pending_assignments: pending_assignment Vec.t;
+  watches: Watches.t;
   mutable last_res: Check_res.t option;
   proof_tracer: Proof.Tracer.t;
   n_conflicts: int Stat.counter;
@@ -36,7 +50,7 @@ type t = {
   n_restarts: int Stat.counter;
 }
 
-and plugin_action = t
+and plugin_action = t * plugin_id
 
 (* FIXME:
    - add [on_add_var: TVar.t -> unit]
@@ -51,12 +65,15 @@ and plugin_action = t
 and plugin =
   | P : {
       st: 'st;
+      id: plugin_id;
       name: string;
       push_level: 'st -> unit;
       pop_levels: 'st -> int -> unit;
       decide: 'st -> TVar.t -> Value.t option;
-      propagate: 'st -> plugin_action -> TVar.t -> Value.t -> unit;
+      on_assign: 'st -> plugin_action -> TVar.t -> Value.t -> unit;
+      on_event: 'st -> plugin_action -> unit:bool -> plugin_event -> unit;
       term_to_var_hooks: 'st -> Term_to_var.hook list;
+      on_add_var: 'st -> TVar.t -> watch_request list;
     }
       -> plugin
 
@@ -71,6 +88,7 @@ let create ?(stats = Stat.create ()) ~arg tst vst ~proof_tracer () : t =
     pending_assignments = Vec.create ();
     term_to_var = Term_to_var.create vst;
     vars_to_decide = Vars_to_decide.create ();
+    watches = Watches.create vst;
     last_res = None;
     proof_tracer;
     n_restarts = Stat.mk_int stats "cdsat.restarts";
@@ -80,6 +98,7 @@ let create ?(stats = Stat.create ()) ~arg tst vst ~proof_tracer () : t =
 
 let[@inline] trail self = self.trail
 let[@inline] iter_plugins self ~f = Vec.iter ~f self.plugins
+let[@inline] get_plugin (self : t) (id : plugin_id) = Vec.get self.plugins id
 let[@inline] tst self = self.tst
 let[@inline] vst self = self.vst
 let[@inline] last_res self = self.last_res
@@ -88,15 +107,35 @@ let[@inline] last_res self = self.last_res
 
 module Plugin = struct
   type t = plugin
-  type builder = TVar.store -> t
+  type builder = id:plugin_id -> TVar.store -> t
 
   let[@inline] name (P p) = p.name
 
-  let make_builder ~name ~create ~push_level ~pop_levels ~decide ~propagate
-      ~term_to_var_hooks () : builder =
-   fun vst ->
+  type nonrec event = plugin_event = ..
+
+  type nonrec watch_request = watch_request =
+    | Watch2 of TVar.t array * event
+    | Watch1 of TVar.t array * event
+
+  let make_builder ~name ~create ~push_level ~pop_levels
+      ?(decide = fun _ _ -> None) ?(on_assign = fun _ _ _ _ -> ())
+      ?(on_event = fun _ _ ~unit:_ _ -> ()) ?(on_add_var = fun _ _ -> [])
+      ?(term_to_var_hooks = fun _ -> []) () : builder =
+   fun ~id vst ->
     let st = create vst in
-    P { name; st; push_level; pop_levels; decide; propagate; term_to_var_hooks }
+    P
+      {
+        name;
+        id;
+        st;
+        push_level;
+        pop_levels;
+        decide;
+        on_assign;
+        on_event;
+        term_to_var_hooks;
+        on_add_var;
+      }
 end
 
 (* backtracking *)
@@ -118,6 +157,7 @@ let pop_levels (self : t) n : unit =
     trail;
     plugins;
     term_to_var = _;
+    watches = _;
     vars_to_decide = _;
     pending_assignments;
     last_res = _;
@@ -149,7 +189,8 @@ let add_term_to_var_hook self h = Term_to_var.add_hook self.term_to_var h
 (* plugins *)
 
 let add_plugin self (pb : Plugin.builder) : unit =
-  let (P p as plugin) = pb self.vst in
+  let id = Vec.size self.plugins in
+  let (P p as plugin) = pb ~id self.vst in
   Vec.push self.plugins plugin;
   List.iter (add_term_to_var_hook self) (p.term_to_var_hooks p.st)
 
@@ -157,8 +198,8 @@ let add_plugin self (pb : Plugin.builder) : unit =
 
 let add_ty (_self : t) ~ty:_ : unit = ()
 
-(* Assign [v <- value] for [reason] at [level].
-   This assignment is delayed. *)
+(** Assign [v <- value] for [reason] at [level].
+    This assignment is delayed. *)
 let assign (self : t) (v : TVar.t) ~(value : Value.t) ~level:v_level ~reason :
     unit =
   Log.debugf 50 (fun k ->
@@ -173,27 +214,37 @@ let raise_conflict (c : Conflict.t) : 'a = raise (E_conflict c)
 
 (* add pending assignments to the trail. This might trigger a conflict
    in case an assignment contradicts an already existing assignment. *)
-let perform_pending_assignments (self : t) : unit =
-  while not (Vec.is_empty self.pending_assignments) do
-    let { var = v; level = v_level; value; reason } =
-      Vec.pop_exn self.pending_assignments
-    in
-    match TVar.value self.vst v with
-    | None ->
-      TVar.assign self.vst v ~value ~level:v_level ~reason;
-      Trail.push_assignment self.trail v
-    | Some value' when Value.equal value value' -> () (* idempotent *)
-    | Some _value' ->
-      (* conflict should only occur on booleans since they're the only
-         propagation-able variables *)
-      assert (Term.has_ty_bool (TVar.term self.vst v));
-      Log.debugf 0 (fun k ->
-          k "TODO: conflict (incompatible values for %a)" (TVar.pp self.vst) v);
-      raise_conflict
-      @@ Conflict.make self.vst ~lit:(TLit.make true v) ~propagate_reason:reason
-           ()
+let perform_pending_assignments_real_ (self : t) : unit =
+  while
+    match Vec.pop self.pending_assignments with
+    | None -> false
+    | Some { var = v; level = v_level; value; reason } ->
+      (match TVar.value self.vst v with
+      | None ->
+        (* assign [v], put it on the trail. Do not notify watchers yet. *)
+        TVar.assign self.vst v ~value ~level:v_level ~reason;
+        Trail.push_assignment self.trail v
+      | Some value' when Value.equal value value' -> () (* idempotent *)
+      | Some _value' ->
+        (* conflict should only occur on booleans since they're the only
+           propagation-able variables *)
+        assert (Term.has_ty_bool (TVar.term self.vst v));
+        Log.debugf 0 (fun k ->
+            k "TODO: conflict (incompatible values for %a)" (TVar.pp self.vst) v);
+        raise_conflict
+        @@ Conflict.make self.vst ~lit:(TLit.make true v)
+             ~propagate_reason:reason ());
+      true
+  do
+    ()
   done
 
+let[@inline] perform_pending_assignments (self : t) : unit =
+  if not (Vec.is_empty self.pending_assignments) then
+    perform_pending_assignments_real_ self
+
+(** Perform unit propagation in theories. Returns [Some c] if [c]
+    is a conflict detected during propagation. *)
 let propagate (self : t) : Conflict.t option =
   let@ () = Profile.with_ "cdsat.propagate" in
   try
@@ -213,7 +264,16 @@ let propagate (self : t) : Conflict.t option =
           | None -> assert false
         in
 
-        iter_plugins self ~f:(fun (P p) -> p.propagate p.st self var value);
+        (* directly give assignment to plugins *)
+        iter_plugins self ~f:(fun (P p) ->
+            p.on_assign p.st (self, p.id) var value;
+            perform_pending_assignments self);
+
+        (* notifier watchers *)
+        Watches.update self.watches var ~f:(fun ~unit (pl_id, ev) ->
+            let (P p) = get_plugin self pl_id in
+            p.on_event p.st (self, p.id) ~unit ev;
+            perform_pending_assignments self);
 
         (* move to next var *)
         Trail.set_head self.trail (Trail.head self.trail + 1)
@@ -234,6 +294,7 @@ let make_sat_res (_self : t) : Check_res.sat_result =
     iter_true_lits = (fun _ -> assert false);
   }
 
+(** Make a decision, or return [`Full_model] *)
 let rec decide (self : t) : [ `Decided | `Full_model ] =
   match Vars_to_decide.pop_next self.vars_to_decide with
   | None -> `Full_model
@@ -260,6 +321,7 @@ let rec decide (self : t) : [ `Decided | `Full_model ] =
         `Decided
     )
 
+(** Solve satisfiability of the current set of assertions *)
 let solve ~on_exit ~on_progress ~should_stop ~assumptions (self : t) :
     Check_res.t =
   let@ () = Profile.with_ "cdsat.solve" in
@@ -319,8 +381,26 @@ let solve ~on_exit ~on_progress ~should_stop ~assumptions (self : t) :
 module Plugin_action = struct
   type t = plugin_action
 
-  let[@inline] propagate (self : t) var value reason : unit =
+  let[@inline] propagate ((self, _) : t) var value reason : unit =
     assign self var ~value ~level:(Reason.level reason) ~reason
 
-  let term_to_var = term_to_var
+  let term_to_var (self, _) t : TVar.t = term_to_var self t
+
+  let watch1 ((self, pl_id) : t) (vars : _ array) (ev : plugin_event) : unit =
+    let _h : Watches.handle =
+      Watches.watch1 self.watches vars (pl_id, ev) ~f:(fun ~unit (_, ev) ->
+          let (P p) = get_plugin self pl_id in
+          p.on_event p.st (self, pl_id) ~unit ev;
+          perform_pending_assignments self)
+    in
+    ()
+
+  let watch2 ((self, pl_id) : t) (vars : _ array) (ev : plugin_event) : unit =
+    let _h : Watches.handle =
+      Watches.watch2 self.watches vars (pl_id, ev) ~f:(fun ~unit (_, ev) ->
+          let (P p) = get_plugin self pl_id in
+          p.on_event p.st (self, pl_id) ~unit ev;
+          perform_pending_assignments self)
+    in
+    ()
 end
diff --git a/src/cdsat/core.mli b/src/cdsat/core.mli
index 7f9caae8..badf5dbf 100644
--- a/src/cdsat/core.mli
+++ b/src/cdsat/core.mli
@@ -11,11 +11,25 @@ end
 
 (** {2 Plugins} *)
 
+type plugin_event = ..
+
+(** Actions passed to plugins *)
 module Plugin_action : sig
   type t
 
   val propagate : t -> TVar.t -> Value.t -> Reason.t -> unit
+  (** Propagate given assignment *)
+
   val term_to_var : t -> Term.t -> TVar.t
+  (** Convert a term to a variable *)
+
+  val watch1 : t -> TVar.t array -> plugin_event -> unit
+  (** Create a watcher for the given set of variables, which will trigger
+      the event *)
+
+  val watch2 : t -> TVar.t array -> plugin_event -> unit
+  (** Create a watcher for the given set of variables, which will trigger
+      the event *)
 end
 
 (** Core plugin *)
@@ -25,14 +39,22 @@ module Plugin : sig
 
   val name : t -> string
 
+  type event = plugin_event = ..
+
+  type watch_request =
+    | Watch2 of TVar.t array * event
+    | Watch1 of TVar.t array * event
+
   val make_builder :
     name:string ->
     create:(TVar.store -> 'st) ->
     push_level:('st -> unit) ->
     pop_levels:('st -> int -> unit) ->
-    decide:('st -> TVar.t -> Value.t option) ->
-    propagate:('st -> Plugin_action.t -> TVar.t -> Value.t -> unit) ->
-    term_to_var_hooks:('st -> Term_to_var.hook list) ->
+    ?decide:('st -> TVar.t -> Value.t option) ->
+    ?on_assign:('st -> Plugin_action.t -> TVar.t -> Value.t -> unit) ->
+    ?on_event:('st -> Plugin_action.t -> unit:bool -> event -> unit) ->
+    ?on_add_var:('st -> TVar.t -> watch_request list) ->
+    ?term_to_var_hooks:('st -> Term_to_var.hook list) ->
     unit ->
     builder
 end
diff --git a/src/cdsat/plugin_bool.ml b/src/cdsat/plugin_bool.ml
index 1eb531d4..6c38184d 100644
--- a/src/cdsat/plugin_bool.ml
+++ b/src/cdsat/plugin_bool.ml
@@ -32,12 +32,13 @@ let decide (self : t) (v : TVar.t) : Value.t option =
     Some (Term.true_ self.tst)
   | _ -> None
 
-let propagate (self : t) (act : Core.Plugin_action.t) (v : TVar.t)
+let on_assign (self : t) (act : Core.Plugin_action.t) (v : TVar.t)
     (value : Value.t) : unit =
   Log.debugf 0 (fun k ->
-      k "(@[bool-plugin.propagate %a@])" (TVar.pp self.vst) v);
+      k "(@[bool-plugin.on-assign %a@])" (TVar.pp self.vst) v);
   ()
-(* TODO: BCP *)
+
+(* TODO: BCP via on_event *)
 
 let term_to_var_hooks (self : t) : _ list =
   let (module A) = self.arg in
@@ -72,4 +73,4 @@ let builder ((module A : ARG) as arg) : Core.Plugin.builder =
     { arg; vst; tst }
   in
   Core.Plugin.make_builder ~name:"bool" ~create ~push_level ~pop_levels ~decide
-    ~propagate ~term_to_var_hooks ()
+    ~on_assign ~term_to_var_hooks ()
diff --git a/src/cdsat/plugin_uninterpreted.ml b/src/cdsat/plugin_uninterpreted.ml
index 759448c1..e169e06d 100644
--- a/src/cdsat/plugin_uninterpreted.ml
+++ b/src/cdsat/plugin_uninterpreted.ml
@@ -35,7 +35,8 @@ let pop_levels self n = Cong_tbl.pop_levels self.cong_table n
 (* let other theories decide, depending on the type *)
 let decide _ _ = None
 
-let propagate (self : t) _act (v : TVar.t) (value : Value.t) =
+(* FIXME: use on_event instead, watch (term + set of args) for congruence *)
+let on_assign (self : t) _act (v : TVar.t) (value : Value.t) =
   match TVar.theory_view self.vst v with
   | Unin_const _ -> ()
   | Unin_fun { f = _; args } ->
@@ -65,4 +66,4 @@ let term_to_var_hooks (self : t) : _ list =
 
 let builder ((module A : ARG) as arg) : Core.Plugin.builder =
   Core.Plugin.make_builder ~name:"uf" ~create:(create arg) ~push_level
-    ~pop_levels ~decide ~propagate ~term_to_var_hooks ()
+    ~pop_levels ~decide ~on_assign ~term_to_var_hooks ()
diff --git a/src/cdsat/watch1.ml b/src/cdsat/watch1.ml
deleted file mode 100644
index 1a9b64e5..00000000
--- a/src/cdsat/watch1.ml
+++ /dev/null
@@ -1,38 +0,0 @@
-open Watch_utils_
-
-type t = { vst: TVar.store; arr: TVar.t array; mutable alive: bool }
-
-let make vst l = { alive = true; vst; arr = Array.of_list l }
-let[@inline] make_a vst arr : t = { alive = true; vst; arr }
-let[@inline] alive self = self.alive
-let[@inline] kill self = self.alive <- false
-
-let[@inline] iter (self : t) k =
-  if Array.length self.arr > 0 then k self.arr.(0)
-
-let init (self : t) t ~on_all_set : unit =
-  let i, all_set = find_watch_ self.vst self.arr 0 0 in
-  (* put watch first *)
-  Util.swap_array self.arr i 0;
-  TVar.add_watcher self.vst self.arr.(0) ~watcher:t;
-  if all_set then on_all_set ();
-  ()
-
-let update (self : t) t ~watch ~on_all_set : Watch_res.t =
-  if self.alive then (
-    (* find another watch. If none is present, keep the
-       current one and call [on_all_set]. *)
-    assert (self.arr.(0) == watch);
-    let i, all_set = find_watch_ self.vst self.arr 0 0 in
-    if all_set then (
-      on_all_set ();
-      Watch_res.Watch_keep (* just keep current watch *)
-    ) else (
-      (* use [i] as the watch *)
-      assert (i > 0);
-      Util.swap_array self.arr i 0;
-      TVar.add_watcher self.vst self.arr.(0) ~watcher:t;
-      Watch_res.Watch_remove
-    )
-  ) else
-    Watch_res.Watch_remove
diff --git a/src/cdsat/watch1.mli b/src/cdsat/watch1.mli
deleted file mode 100644
index aa26a63f..00000000
--- a/src/cdsat/watch1.mli
+++ /dev/null
@@ -1,29 +0,0 @@
-(** 1-Watch Scheme *)
-
-type t
-
-val make : TVar.store -> TVar.t list -> t
-
-val make_a : TVar.store -> TVar.t array -> t
-(** owns the array *)
-
-val alive : t -> bool
-val kill : t -> unit
-
-val iter : t -> TVar.t Iter.t
-(** current watch(es) *)
-
-val init : t -> TVar.t -> on_all_set:(unit -> unit) -> unit
-(** [init w t ~on_all_set] initializes [w] (the watchlist) for
-    var [t], by finding an unassigned TVar.t in the watchlist and
-    registering [t] to it.
-    If all vars are set, then it watches the one with the highest level
-    and call [on_all_set ()]
-  *)
-
-val update :
-  t -> TVar.t -> watch:TVar.t -> on_all_set:(unit -> unit) -> Watch_res.t
-(** [update w t ~watch ~on_all_set] updates [w] after [watch]
-    has been assigned. It looks for another TVar.t in [w] for [t] to watch.
-    If all vars are set, then it calls [on_all_set ()]
-*)
diff --git a/src/cdsat/watch2.ml b/src/cdsat/watch2.ml
deleted file mode 100644
index b25765c1..00000000
--- a/src/cdsat/watch2.ml
+++ /dev/null
@@ -1,61 +0,0 @@
-open Watch_utils_
-
-type t = { vst: TVar.store; arr: TVar.t array; mutable alive: bool }
-
-let dummy = [||]
-let make vst l : t = { alive = true; vst; arr = Array.of_list l }
-let[@inline] make_a vst arr : t = { vst; arr; alive = true }
-let[@inline] alive self = self.alive
-let[@inline] kill self = self.alive <- false
-
-let[@inline] iter (self : t) k =
-  if Array.length self.arr > 0 then (
-    k self.arr.(0);
-    if Array.length self.arr > 1 then k self.arr.(1)
-  )
-
-let init (self : t) t ~on_unit ~on_all_set : unit =
-  let i0, all_set0 = find_watch_ self.vst self.arr 0 0 in
-  Util.swap_array self.arr i0 0;
-  let i1, all_set1 = find_watch_ self.vst self.arr 1 0 in
-  Util.swap_array self.arr i1 1;
-  TVar.add_watcher self.vst self.arr.(0) ~watcher:t;
-  TVar.add_watcher self.vst self.arr.(1) ~watcher:t;
-  assert (
-    if all_set0 then
-      all_set1
-    else
-      true);
-  if all_set0 then
-    on_all_set ()
-  else if all_set1 then (
-    assert (not (TVar.has_value self.vst self.arr.(0)));
-    on_unit self.arr.(0)
-  );
-  ()
-
-let update (self : t) t ~watch ~on_unit ~on_all_set : Watch_res.t =
-  if self.alive then (
-    (* find another watch. If none is present, keep the
-       current ones and call [on_unit] or [on_all_set]. *)
-    if self.arr.(0) == watch then
-      (* ensure that if there is only one watch, it's the first *)
-      Util.swap_array self.arr 0 1
-    else
-      assert (self.arr.(1) == watch);
-    let i, all_set1 = find_watch_ self.vst self.arr 1 0 in
-    if all_set1 then (
-      if TVar.has_value self.vst self.arr.(0) then
-        on_all_set ()
-      else
-        on_unit self.arr.(0);
-      Watch_res.Watch_keep (* just keep current watch *)
-    ) else (
-      (* use [i] as the second watch *)
-      assert (i > 1);
-      Util.swap_array self.arr i 1;
-      TVar.add_watcher self.vst self.arr.(1) ~watcher:t;
-      Watch_res.Watch_remove
-    )
-  ) else
-    Watch_res.Watch_remove
diff --git a/src/cdsat/watch2.mli b/src/cdsat/watch2.mli
deleted file mode 100644
index 3400ab5f..00000000
--- a/src/cdsat/watch2.mli
+++ /dev/null
@@ -1,40 +0,0 @@
-(** 2-Watch Scheme *)
-
-type t
-
-val make : TVar.store -> TVar.t list -> t
-
-val make_a : TVar.store -> TVar.t array -> t
-(** owns the array *)
-
-val iter : t -> TVar.t Iter.t
-(** current watch(es) *)
-
-val kill : t -> unit
-(** Disable the watch. It will be removed lazily. *)
-
-val alive : t -> bool
-(** Is the watch alive? *)
-
-val init :
-  t -> TVar.t -> on_unit:(TVar.t -> unit) -> on_all_set:(unit -> unit) -> unit
-(** [init w t ~on_all_set] initializes [w] (the watchlist) for
-    var [t], by finding an unassigned var in the watchlist and
-    registering [t] to it.
-    If exactly one TVar.t [u] is not set, then it calls [on_unit u].
-    If all vars are set, then it watches the one with the highest level
-    and call [on_all_set ()]
-  *)
-
-val update :
-  t ->
-  TVar.t ->
-  watch:TVar.t ->
-  on_unit:(TVar.t -> unit) ->
-  on_all_set:(unit -> unit) ->
-  Watch_res.t
-(** [update w t ~watch ~on_all_set] updates [w] after [watch]
-    has been assigned. It looks for another var in [w] for [t] to watch.
-    If exactly one var [u] is not set, then it calls [on_unit u].
-    If all vars are set, then it calls [on_all_set ()]
-*)
diff --git a/src/cdsat/watch_res.ml b/src/cdsat/watch_res.ml
deleted file mode 100644
index f14eeee8..00000000
--- a/src/cdsat/watch_res.ml
+++ /dev/null
@@ -1,3 +0,0 @@
-type t =
-  | Watch_keep  (** Keep the watch *)
-  | Watch_remove  (** Remove the watch *)
diff --git a/src/cdsat/watch_schemes.ml b/src/cdsat/watch_schemes.ml
new file mode 100644
index 00000000..9823f956
--- /dev/null
+++ b/src/cdsat/watch_schemes.ml
@@ -0,0 +1,186 @@
+type watch_update_res =
+  | Watch_keep  (** Keep the watch *)
+  | Watch_remove  (** Remove the watch *)
+
+(* find a term in [w] that is not assigned, or otherwise,
+   the one with highest level
+   @return index of term to watch, and [true] if all are assigned *)
+let find_watch_ tst w ~idx0 : int * bool =
+  let rec loop i idx_with_highest_level =
+    if i = Array.length w then
+      idx_with_highest_level, true
+    else if TVar.has_value tst w.(i) then (
+      let idx_with_highest_level =
+        if TVar.level tst w.(i) > TVar.level tst w.(idx_with_highest_level) then
+          i
+        else
+          idx_with_highest_level
+      in
+      loop (i + 1) idx_with_highest_level
+    ) else
+      i, false
+  in
+  loop idx0 0
+
+module Make (Ev : sig
+  type t
+end) =
+struct
+  type handle = int
+
+  module Handle_v_map = TVar.Dense_map (struct
+    type t = Veci.t
+
+    let create () = Veci.create ~cap:2 ()
+  end)
+
+  type watch =
+    | No_watch
+    | Watch1 of { ev: Ev.t; arr: TVar.t array }
+    | Watch2 of { ev: Ev.t; arr: TVar.t array }
+
+  type t = {
+    vst: TVar.store;
+    watches: watch Vec.t;
+    by_var: Handle_v_map.t;
+        (** maps a variable to the handles of its watchers *)
+    alive: Bitvec.t;
+    free_slots: Veci.t;
+  }
+
+  let create vst : t =
+    {
+      vst;
+      watches = Vec.create ();
+      by_var = Handle_v_map.create ();
+      alive = Bitvec.create ();
+      free_slots = Veci.create ();
+    }
+
+  type cb_ = unit:bool -> Ev.t -> unit
+
+  (* allocate new watch *)
+  let make_watch_ (self : t) (w : watch) : handle =
+    if Veci.is_empty self.free_slots then (
+      let h = Vec.size self.watches in
+      Vec.push self.watches w;
+      Bitvec.ensure_size self.alive (h + 1);
+      Bitvec.set self.alive h true;
+      h
+    ) else (
+      let h = Veci.pop self.free_slots in
+      Bitvec.set self.alive h true;
+      Vec.set self.watches h w;
+      h
+    )
+
+  (* [h] is currently watching [v] *)
+  let set_watch (self : t) (v : TVar.t) (h : handle) : unit =
+    let vec = Handle_v_map.get self.by_var v in
+    Veci.push vec h
+
+  let watch1 (self : t) (arr : TVar.t array) (ev : Ev.t) ~(f : cb_) : handle =
+    let h = make_watch_ self (Watch1 { arr; ev }) in
+    let i, all_set = find_watch_ self.vst arr ~idx0:0 in
+    (* put watched var first *)
+    Util.swap_array arr i 0;
+    set_watch self arr.(0) h;
+    if all_set then f ~unit:false ev;
+    h
+
+  let watch2 (self : t) (arr : TVar.t array) (ev : Ev.t) ~(f : cb_) : handle =
+    let h = make_watch_ self (Watch2 { arr; ev }) in
+    (* put watched vars first *)
+    let i0, all_set0 = find_watch_ self.vst arr ~idx0:0 in
+    Util.swap_array arr i0 0;
+    let i1, all_set1 = find_watch_ self.vst arr ~idx0:1 in
+    Util.swap_array arr i1 1;
+    set_watch self arr.(0) h;
+    set_watch self arr.(1) h;
+    assert (
+      if all_set0 then
+        all_set1
+      else
+        true);
+    if all_set0 then
+      f ~unit:false ev
+    else if all_set1 then (
+      assert (not (TVar.has_value self.vst arr.(0)));
+      f ~unit:true ev
+    );
+    h
+
+  (** disable watch. It will be removed from watchers next time they
+      are updated or next time {!gc} is called. *)
+  let kill (self : t) (h : handle) : unit =
+    if Bitvec.get self.alive h then (
+      Vec.set self.watches h No_watch;
+      Bitvec.set self.alive h false
+    )
+
+  let[@inline] alive (self : t) (h : handle) : bool = Bitvec.get self.alive h
+
+  let gc (self : t) : unit =
+    (* first, filter all dead watches from [self.by_var] *)
+    Handle_v_map.iter self.by_var ~f:(fun _v handles ->
+        Veci.filter_in_place (alive self) handles);
+    (* then, mark the dead watch slots for reuse *)
+    Vec.iteri self.watches ~f:(fun i _w ->
+        if not (alive self i) then Veci.push self.free_slots i)
+
+  (* update a single watch *)
+  let update1 (self : t) (h : handle) (w : watch) ~updated_var ~f :
+      watch_update_res =
+    match w with
+    | No_watch -> Watch_remove
+    | _ when not (alive self h) -> Watch_remove
+    | Watch1 { arr; ev } ->
+      (* find another watch. If none is present, keep the
+         current one and call [f]. *)
+      assert (TVar.equal arr.(0) updated_var);
+      let i, all_set = find_watch_ self.vst arr ~idx0:0 in
+      if all_set then (
+        f ~unit:false ev;
+        Watch_keep (* just keep current watch *)
+      ) else (
+        (* use [i] as the watch *)
+        assert (i > 0);
+        Util.swap_array arr i 0;
+        set_watch self arr.(0) h;
+        Watch_remove
+      )
+    | Watch2 { arr; ev } ->
+      (* find another watch. If none is present, keep the
+         current ones and call [f]. *)
+      if TVar.equal arr.(0) updated_var then
+        (* ensure that if there is only one watch, it's the first *)
+        Util.swap_array arr 0 1
+      else
+        assert (TVar.equal arr.(1) updated_var);
+      let i, all_set1 = find_watch_ self.vst arr ~idx0:1 in
+      if all_set1 then (
+        if TVar.has_value self.vst arr.(0) then
+          f ~unit:false ev
+        else
+          f ~unit:true ev;
+        (* just keep current watch *)
+        Watch_keep
+      ) else (
+        (* use [i] as the second watch *)
+        assert (i > 1);
+        Util.swap_array arr i 1;
+        set_watch self arr.(1) h;
+        Watch_remove
+      )
+
+  let update (self : t) (v : TVar.t) ~(f : cb_) : unit =
+    let vec = Handle_v_map.get self.by_var v in
+    let i = ref 0 in
+    while !i < Veci.size vec do
+      let handle = Veci.get vec !i in
+      let w = Vec.get self.watches handle in
+      match update1 self handle w ~updated_var:v ~f with
+      | Watch_keep -> incr i
+      | Watch_remove -> Veci.fast_remove vec !i
+    done
+end
diff --git a/src/cdsat/watch_schemes.mli b/src/cdsat/watch_schemes.mli
new file mode 100644
index 00000000..4ec51f14
--- /dev/null
+++ b/src/cdsat/watch_schemes.mli
@@ -0,0 +1,31 @@
+(** Watch schemes *)
+
+module Make (Ev : sig
+  type t
+end) : sig
+  type t
+  type handle
+
+  val create : TVar.store -> t
+  (** New set of watchers *)
+
+  val watch2 :
+    t -> TVar.t array -> Ev.t -> f:(unit:bool -> Ev.t -> unit) -> handle
+  (** 2-watch scheme on these variables. *)
+
+  val watch1 :
+    t -> TVar.t array -> Ev.t -> f:(unit:bool -> Ev.t -> unit) -> handle
+  (** 1-watch scheme on these variables. *)
+
+  val kill : t -> handle -> unit
+  (** Disable watch *)
+
+  val gc : t -> unit
+  (** Reclaim slots that have been killed *)
+
+  val update : t -> TVar.t -> f:(unit:bool -> Ev.t -> unit) -> unit
+  (** [update watches v ~f] updates watchers that contain [v],
+      and calls [f ~unit ev] for each event whose watch just saturated.
+      [unit] is true if the watch is a 2-watch that became unit; [false] in
+      any other case (including a fully saturated 2-watch) *)
+end
diff --git a/src/cdsat/watch_utils_.ml b/src/cdsat/watch_utils_.ml
deleted file mode 100644
index fd3ea00d..00000000
--- a/src/cdsat/watch_utils_.ml
+++ /dev/null
@@ -1,16 +0,0 @@
-(* find a term in [w] that is not assigned, or otherwise,
-   the one with highest level
-   @return index of term to watch, and [true] if all are assigned *)
-let rec find_watch_ tst w i highest : int * bool =
-  if i = Array.length w then
-    highest, true
-  else if TVar.has_value tst w.(i) then (
-    let highest =
-      if TVar.level tst w.(i) > TVar.level tst w.(highest) then
-        i
-      else
-        highest
-    in
-    find_watch_ tst w (i + 1) highest
-  ) else
-    i, false