diff --git a/fieldglass.ml b/fieldglass.ml
index 81ed814..421c9ab 100644
--- a/fieldglass.ml
+++ b/fieldglass.ml
@@ -5,3 +5,7 @@ let lens ~view ~set = view, set
 let view (get, _) = get
 let set (_, put) = put
 let over (get, put) ~f source = put (f (get source)) source
+
+let compose (outer_get, outer_put) (inner_get, inner_put) =
+  (fun source -> inner_get (outer_get source)),
+  (fun value source -> outer_put (inner_put value (outer_get source)) source)
diff --git a/fieldglass.mli b/fieldglass.mli
index 75190ad..b220337 100644
--- a/fieldglass.mli
+++ b/fieldglass.mli
@@ -5,3 +5,4 @@ val lens : view:('s -> 'a) -> set:('b -> 's -> 't) -> ('s, 't, 'a, 'b) lens
 val view : ('s, 't, 'a, 'b) lens -> 's -> 'a
 val set : ('s, 't, 'a, 'b) lens -> 'b -> 's -> 't
 val over : ('s, 't, 'a, 'b) lens -> f:('a -> 'b) -> 's -> 't
+val compose : ('s, 't, 'a, 'b) lens -> ('a, 'b, 'c, 'd) lens -> ('s, 't, 'c, 'd) lens
diff --git a/runtime.ml b/runtime.ml
index 9027da9..d858005 100644
--- a/runtime.ml
+++ b/runtime.ml
@@ -13,3 +13,10 @@ let () =
   let calls = ref 0 in
   assert (over sample ~f:(fun text -> incr calls; text ^ "s") source = ("colours", true));
   assert (!calls = 1)
+
+let () =
+  let first = (fst, fun value (_, rest) -> value, rest) in
+  let second = (snd, fun value (rest, _) -> rest, value) in
+  let focus = compose first second in
+  assert (view focus ((true, "grey"), false) = "grey");
+  assert (set focus 9 ((true, "grey"), false) = ((true, 9), false))