diff --git a/src/cdsat/vars_to_decide.ml b/src/cdsat/vars_to_decide.ml
new file mode 100644
index 00000000..a234792f
--- /dev/null
+++ b/src/cdsat/vars_to_decide.ml
@@ -0,0 +1,74 @@
+module V = TVar
+
+type node = { var: V.t; mutable next: node; mutable prev: node }
+type t = { vars: node V.Tbl.t; mutable first: node option }
+
+let create () : t = { vars = V.Tbl.create 32; first = None }
+let[@inline] size (self : t) : int = V.Tbl.length self.vars
+let[@inline] mem (self : t) (v : V.t) : bool = V.Tbl.mem self.vars v
+
+let add (self : t) (v : V.t) : unit =
+  if not (V.Tbl.mem self.vars v) then (
+    let rec node = { var = v; prev = node; next = node } in
+    V.Tbl.add self.vars v node;
+    match self.first with
+    | None -> self.first <- Some node
+    | Some n_first ->
+      (* insert at the end *)
+      n_first.prev.next <- node;
+      n_first.prev <- node;
+      node.prev <- n_first.prev;
+      node.next <- n_first
+  )
+
+let pop_next (self : t) : _ option =
+  match self.first with
+  | None -> None
+  | Some n ->
+    let next = n.next in
+    (* remove [n] from the list *)
+    next.prev <- n.prev;
+    n.prev.next <- next;
+
+    (* point to the next *)
+    if next != n then
+      self.first <- Some next
+    else
+      self.first <- None;
+
+    Some n.var
+
+let bump (self : t) (v : V.t) : unit =
+  match V.Tbl.find_opt self.vars v with
+  | None -> ()
+  | Some node ->
+    (* move node to front *)
+    node.next.prev <- node.prev;
+    node.prev.next <- node.next;
+
+    let first =
+      match self.first with
+      | Some n -> n
+      | None -> assert false
+    in
+
+    node.prev <- first.prev;
+    node.next <- first;
+    first.prev <- node;
+    first.next.prev <- node;
+    self.first <- Some node
+
+let remove (self : t) (v : V.t) : unit =
+  match V.Tbl.find_opt self.vars v with
+  | None -> ()
+  | Some node ->
+    (* remove from list *)
+    node.prev.next <- node.next;
+    node.next.prev <- node.prev;
+
+    (match self.first with
+    | Some n when n == node -> self.first <- Some node.next
+    | _ -> ());
+
+    (* remove from table *)
+    V.Tbl.remove self.vars v
diff --git a/src/cdsat/vars_to_decide.mli b/src/cdsat/vars_to_decide.mli
new file mode 100644
index 00000000..91e24d0d
--- /dev/null
+++ b/src/cdsat/vars_to_decide.mli
@@ -0,0 +1,19 @@
+(** Set of variables yet to decide *)
+
+type t
+
+val create : unit -> t
+val mem : t -> TVar.t -> bool
+val size : t -> int
+
+val add : t -> TVar.t -> unit
+(** Add a variable to the set *)
+
+val bump : t -> TVar.t -> unit
+(** [bump set v] makes [v] more likely to be decided sooner than later. *)
+
+val pop_next : t -> TVar.t option
+(** Pop next variable *)
+
+val remove : t -> TVar.t -> unit
+(** Remove the variable from the set *)