diff --git a/Project.toml b/Project.toml
index accd6fb..b1bc07e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Functors"
 uuid = "d9f16b24-f501-4c13-a1f2-28368ffc5196"
 authors = ["Mike J Innes <mike.j.innes@gmail.com>"]
-version = "0.2.5"
+version = "0.2.6"
 
 [compat]
 julia = "1"
diff --git a/src/functor.jl b/src/functor.jl
index b502493..b08acf7 100644
--- a/src/functor.jl
+++ b/src/functor.jl
@@ -149,7 +149,8 @@ fmapstructure(f, x; kwargs...) = fmap(f, x; walk = (f, x) -> map(f, children(x))
     fcollect(x; exclude = v -> false)
 
 Traverse `x` by recursing each child of `x` as defined by [`functor`](@ref)
-and collecting the results into a flat array.
+and collecting the results into a flat array, ordered by a breadth-first
+traversal of `x`, respecting the iteration order of `children` calls.
 
 Doesn't recurse inside branches rooted at nodes `v`
 for which `exclude(v) == true`.
@@ -192,11 +193,15 @@ julia> fcollect(m, exclude = v -> Functors.isleaf(v))
  Bar([1, 2, 3])
 ```
 """
-function fcollect(x; cache = [], exclude = v -> false)
-  x in cache && return cache
-  if !exclude(x)
-    push!(cache, x)
-    foreach(y -> fcollect(y; cache = cache, exclude = exclude), children(x))
-  end
-  return cache
+function fcollect(x; output = [], cache = Base.IdSet(), exclude = v -> false)
+    # note: we don't have an `OrderedIdSet`, so we use an `IdSet` for the cache
+    # (to ensure we get exactly 1 copy of each distinct array), and a usual `Vector`
+    # for the results, to preserve traversal order (important downstream!).
+    x in cache && return output
+    if !exclude(x)
+      push!(cache, x)
+      push!(output, x)
+      foreach(y -> fcollect(y; cache=cache, output=output, exclude=exclude), children(x))
+    end
+    return output
 end
diff --git a/test/basics.jl b/test/basics.jl
index bc1617b..9d1ce76 100644
--- a/test/basics.jl
+++ b/test/basics.jl
@@ -84,6 +84,11 @@ end
   m3 = Foo(m2, m0)
   m4 = Bar(m3)
   @test all(fcollect(m4) .=== [m4, m3, m2, m1, m0])
+
+  m1 = [1, 2, 3]
+  m2 = [1, 2, 3]
+  m3 = Foo(m1, m2)
+  @test all(fcollect(m3) .=== [m3, m1, m2])
 end
 
 struct FFoo