diff --git a/bij.ml b/bij.ml
index 3f0bf337..916448d9 100644
--- a/bij.ml
+++ b/bij.ml
@@ -39,7 +39,7 @@ type _ t =
   | Map : ('a -> 'b) * ('b -> 'a) * 'b t -> 'a t
   | Switch : ('a -> char * 'a inject_branch) * (char -> 'a extract_branch) -> 'a t
 and _ inject_branch =
-  | BranchTo : 'b t * 'b * 'a -> 'a inject_branch
+  | BranchTo : 'b t * 'b -> 'a inject_branch
 and _ extract_branch =
   | BranchFrom : 'b t * ('b -> 'a) -> 'a extract_branch
 
@@ -275,7 +275,7 @@ module SexpEncode(Sink : SINK) = struct
         let y = inject x in
         encode bij' y
       | Switch (inject, _), x ->
-        let c, BranchTo (bij', y, _) = inject x in
+        let c, BranchTo (bij', y) = inject x in
         Sink.write_char sink c;
         encode bij' y
     in encode bij x
diff --git a/bij.mli b/bij.mli
index d880985d..c8c193ea 100644
--- a/bij.mli
+++ b/bij.mli
@@ -44,16 +44,16 @@ val triple : 'a t -> 'b t -> 'c t -> ('a * 'b * 'c) t
 val map : inject:('a -> 'b) -> extract:('b -> 'a) -> 'b t -> 'a t
 
 type _ inject_branch =
-  | BranchTo : 'b t * 'b * 'a -> 'a inject_branch
+  | BranchTo : 'b t * 'b -> 'a inject_branch
 type _ extract_branch =
   | BranchFrom : 'b t * ('b -> 'a) -> 'a extract_branch
 
 val switch : inject:('a -> char * 'a inject_branch) ->
              extract:(char -> 'a extract_branch) -> 'a t
-  (** discriminates based on the next character. 
-      The selection function, with type ['a -> char], is used to select a
-      bijection depending on the value.
-      ' ' means "default" *)
+  (** Discriminates unions based on the next character.
+      [inject] is used to select a character, as well as mapping to another
+      type (the argument of the algebraic constructor);
+      [extract] retrieves which type to parse based on the character. *)
 
 exception EOF
 
diff --git a/tests/test_bij.ml b/tests/test_bij.ml
index f7c2d61a..81dec3e0 100644
--- a/tests/test_bij.ml
+++ b/tests/test_bij.ml
@@ -34,10 +34,10 @@ type term =
 let bij_term =
   let rec mk_bij () =
     switch
-    ~inject:(fun t -> match t with
-      | Const s -> 'c', BranchTo (string_, s, t)
-      | Int i -> 'i', BranchTo (int_, i, t)
-      | App l -> 'a', BranchTo (list_ (mk_bij ()), l, t))
+    ~inject:(function
+      | Const s -> 'c', BranchTo (string_, s)
+      | Int i -> 'i', BranchTo (int_, i)
+      | App l -> 'a', BranchTo (list_ (mk_bij ()), l))
     ~extract:(function
       | 'c' -> BranchFrom (string_, fun x -> Const x)
       | 'i' -> BranchFrom (int_, fun x -> Int x)