diff --git a/Project.toml b/Project.toml
index 733172a0..b7e70ed5 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRulesTestUtils"
 uuid = "cdddcdb0-9152-4a09-a978-84456f9df70a"
-version = "0.6.8"
+version = "0.6.9"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/src/testers.jl b/src/testers.jl
index 5505d45f..ad02defc 100644
--- a/src/testers.jl
+++ b/src/testers.jl
@@ -114,8 +114,7 @@ function test_frule(
         Ω = f(deepcopy(xs)...; deepcopy(fkwargs)...)
         check_equal(Ω_ad, Ω; isapprox_kwargs...)
 
-        # TODO: remove Nothing when https://github.com/JuliaDiff/ChainRulesTestUtils.jl/issues/113
-        ẋs_is_ignored = isa.(ẋs, Union{Nothing, DoesNotExist})
+        ẋs_is_ignored = _ignore.(ẋs)
         if any(ẋs .== nothing)
             Base.depwarn(
                 "test_frule(f, k ⊢ nothing) is deprecated, use " *
@@ -191,8 +190,7 @@ function test_rrule(
         @test ∂self === NO_FIELDS  # No internal fields
 
         # Correctness testing via finite differencing.
-        # TODO: remove Nothing when https://github.com/JuliaDiff/ChainRulesTestUtils.jl/issues/113
-        x̄s_is_dne = isa.(accumulated_x̄, Union{Nothing, DoesNotExist})
+        x̄s_is_ignored = _ignore.(accumulated_x̄)
         if any(accumulated_x̄ .== nothing)
             Base.depwarn(
                 "test_rrule(f, k ⊢ nothing) is deprecated, use " *
@@ -201,9 +199,9 @@ function test_rrule(
             )
         end
 
-        x̄s_fd = _make_j′vp_call(fdm, (xs...) -> f(xs...; fkwargs...), ȳ, xs, x̄s_is_dne)
+        x̄s_fd = _make_j′vp_call(fdm, (xs...) -> f(xs...; fkwargs...), ȳ, xs, x̄s_is_ignored)
         for (accumulated_x̄, x̄_ad, x̄_fd) in zip(accumulated_x̄, x̄s_ad, x̄s_fd)
-            if accumulated_x̄ isa Union{Nothing, DoesNotExist}  # then we marked this argument as not differentiable # TODO remove once #113
+            if _ignore(accumulated_x̄) # then we marked this argument as not differentiable
                 @assert x̄_fd === nothing  # this is how `_make_j′vp_call` works
                 x̄_ad isa Zero && error(
                     "The pullback in the rrule for $f function should use DoesNotExist()" *
@@ -245,6 +243,16 @@ function _ensure_not_running_on_functor(f, name)
     end
 end
 
+"""
+    _ignore(x) -> Bool
+
+Returns true for tangents we want to ignore in finite differencing, and false otherwise.
+"""
+_ignore(::Any) = false
+_ignore(::DoesNotExist) = true
+_ignore(::Nothing) = true # TODO: remove Nothing when https://github.com/JuliaDiff/ChainRulesTestUtils.jl/issues/113
+_ignore(c::Composite) = all([d === DoesNotExist() for d in c])
+
 """
     _test_inferred(f, args...; kwargs...)
 
diff --git a/test/testers.jl b/test/testers.jl
index 4eb6693f..6f21ec0f 100644
--- a/test/testers.jl
+++ b/test/testers.jl
@@ -526,4 +526,23 @@ end
         test_frule(f_notimplemented, randn(), randn())
         test_rrule(f_notimplemented, randn(), randn())
     end
+
+    @testset "ignore Composites fully made of DoesNotExist" begin
+        mygetindex(x, ind) = x[ind]
+        function ChainRulesCore.rrule(::typeof(mygetindex), x, ind)
+            function myfunc_pullback(Δy)
+                xgrad = zero(x)
+                xgrad[ind] = Δy
+                return NO_FIELDS, xgrad, DoesNotExist()
+            end
+            return mygetindex(x, ind), myfunc_pullback
+        end
+
+        # test that Composites made only of DoesNotExist() are ignored in finite differencing
+        test_rrule(mygetindex, [1, 2, 3, 4, 5.0], 1:2 ⊢ Composite{UnitRange{Int64}}(start=DoesNotExist(), stop=DoesNotExist()))
+
+        # rand_tangent also returns Composites with all DoesNotExist()
+        test_rrule(mygetindex, [1, 2, 3, 4, 5.0], 1:2)
+        test_rrule(mygetindex, [1, 2, 3, 4, 5.0], 1:2:4)
+    end
 end