diff --git a/src/functor.jl b/src/functor.jl
index 67f56ec..df9e31b 100644
--- a/src/functor.jl
+++ b/src/functor.jl
@@ -40,14 +40,24 @@ function _default_walk(f, x)
 end
 
 usecache(x) = !isbits(x)
+usecache(x::Union{String, Symbol}) = false
 
 struct NoKeyword end
 
 function fmap(f, x; exclude = isleaf, walk = _default_walk, cache = usecache(x) ? IdDict() : nothing, prune = NoKeyword())
-  usecache(x) && haskey(cache, x) && return prune isa NoKeyword ? cache[x] : prune
-  xnew = exclude(x) ? f(x) : walk(x -> fmap(f, x; exclude=exclude, walk=walk, cache=cache, prune=prune), x)
-  usecache(x) && setindex!(cache, xnew, x)
-  return xnew
+  if exclude(x)
+    if usecache(x)
+      if haskey(cache, x)
+        prune isa NoKeyword ? cache[x] : prune
+      else
+        cache[x] = f(x)
+      end
+    else
+      f(x)
+    end
+  else
+    walk(x -> fmap(f, x; exclude = exclude, walk = walk, cache = cache, prune = prune), x)
+  end
 end
 
 ###
@@ -73,11 +83,20 @@ end
 ### Vararg forms
 ###
 
-function fmap(f, x, ys...; exclude = isleaf, walk = _default_walk, cache = IdDict(), prune = NoKeyword())
-  usecache(x) && haskey(cache, x) && return prune isa NoKeyword ? cache[x] : prune
-  xnew = exclude(x) ? f(x, ys...) : walk((xy...,) -> fmap(f, xy...; exclude=exclude, walk=walk, cache=cache, prune=prune), x, ys...)
-  usecache(x) && setindex!(cache, xnew, x)
-  return xnew
+function fmap(f, x, ys...; exclude = isleaf, walk = _default_walk, cache = usecache(x) ? IdDict() : nothing, prune = NoKeyword())
+  if exclude(x)
+    if usecache(x)
+      if haskey(cache, x)
+        prune isa NoKeyword ? cache[x] : prune
+      else
+        cache[x] = f(x, ys...)
+      end
+    else
+      f(x, ys...)
+    end
+  else
+    walk((xy...,) -> fmap(f, xy...; exclude = exclude, walk = walk, cache = cache, prune = prune), x, ys...)
+  end
 end
 
 function _default_walk(f, x, ys...)
diff --git a/test/basics.jl b/test/basics.jl
index 6ce8f94..c771098 100644
--- a/test/basics.jl
+++ b/test/basics.jl
@@ -14,6 +14,7 @@ struct NoChildren2; x; y; end
 
 struct NoChild{T}; x::T; end
 
+
 ###
 ### Basic functionality
 ###
@@ -56,13 +57,13 @@ end
   m1p = fmapstructure(identity, m1; prune = nothing)
   @test m1p == (x = [1, 2, 3], y = (x = [1, 2, 3], y = (x = nothing, y = [1, 2, 3])))
 
-  # A non-leaf node can also be repeated:
+  # The cache applies only to leaf nodes, so that "4" is not shared:
   m2 = Foo(Foo(shared, 4), Foo(shared, 4))
   @test m2.x === m2.y
   m2f = fmap(float, m2)
   @test m2f.x.x === m2f.y.x
   m2p = fmapstructure(identity, m2; prune = Bar(0))
-  @test m2p == (x = (x = [1, 2, 3], y = 4), y = Bar(0))
+  @test m2p == (x = (x = [1, 2, 3], y = 4), y = (x = Bar{Int64}(0), y = 4))
 
   # Repeated isbits types should not automatically be regarded as shared:
   m3 = Foo(Foo(shared, 1:3), Foo(1:3, shared))
@@ -75,15 +76,18 @@ end
   @test_skip 0 == @allocated fmap(float, (x=1, y=(2, 3), z=4:5))
 
   @testset "usecache" begin
+    # Leaf types:
     @test usecache([1,2])
-    @test usecache(Ref(3))
-
     @test !usecache(4.0)
+    @test usecache(NoChild([1,2]))
+    @test !usecache(NoChild((3,4)))
+
+    # Not leaf by default, but `exclude` can change that:
+    @test usecache(Ref(3))
     @test !usecache((5, 6.0))
     @test !usecache((a = 2pi, b = missing))
 
-    @test usecache(Bar([1,2]))
-    @test !usecache(Bar((3,4)))
+    @test usecache((x = [1,2,3], y = 4))
   end
 end