diff --git a/src/stage1/generated.jl b/src/stage1/generated.jl
index c1624046..9f84bc88 100644
--- a/src/stage1/generated.jl
+++ b/src/stage1/generated.jl
@@ -225,6 +225,25 @@ function (::∂⃖{N})(f::T, args...) where {T, N}
         end
     end
 end
+function (::∂⃖{N})(::typeof(Core.kwcall), kwargs, f::T, args...) where {T, N}
+    if N == 1
+        # Base case (inlined to avoid ambiguities with manually specified
+        # higher order rules)
+        z = rrule(DiffractorRuleConfig(), KwFunc(f), kwargs, f, args...)
+        if z === nothing
+            return ∂⃖recurse{1}()(f, args..., kwargs...)
+        end
+        return z
+    else
+        ∂⃖p = ∂⃖{N-1}()
+        @destruct z, z̄ = ∂⃖p(rrule, f, args...; kwargs...)
+        if z === nothing
+            return ∂⃖recurse{N}()(f, args...; kwargs...)
+        else
+            return ∂⃖rrule{N}()(z, z̄)
+        end
+    end
+end
 
 function ChainRulesCore.rrule_via_ad(::DiffractorRuleConfig, f::T, args...) where {T}
     Tuple{Any, Any}(∂⃖{1}()(f, args...))
@@ -244,6 +263,10 @@ struct KwFunc{T,S}
 end
 (kw::KwFunc)(args...) = kw.kwf(args...)
 
+function ChainRulesCore.rrule(::typeof(Core.kwcall), kwargs, f, args...)
+    rrule(KwFunc(f), kwargs, f, args...)
+end
+
 function ChainRulesCore.rrule(::typeof(Core.kwfunc), f)
     KwFunc(f), Δ->(NoTangent(), Δ)
 end
diff --git a/test/gradcheck.jl b/test/gradcheck.jl
index d003c82d..f3bb8e9a 100644
--- a/test/gradcheck.jl
+++ b/test/gradcheck.jl
@@ -99,10 +99,11 @@ end
     @test gradcheck(x -> sum(i->x[i], 1:length(x)), randn(10)) #  issue #231
     @test gradcheck(x -> sum((i->x[i]).(1:length(x))), randn(10))
     @test gradcheck(X -> sum(x -> x^2, X), randn(10))
+    @test jacobicheck(x -> sum(x, dims = (2, 3)), (3,4,5))
+    @test jacobicheck(x -> sum(abs2, x; dims=1), randn(4, 3, 2))
 
     # MethodError: no method matching copy(::Nothing)
-    @test_broken jacobicheck(x -> sum(x, dims = (2, 3)), (3,4,5))
-    @test_broken jacobicheck(x -> sum(abs2, x; dims=1), randn(4, 3, 2))
+    # TODO: interesting that this is the only one that is not fixed
     @test_broken gradcheck(X -> sum(sum(x -> x^2, X; dims=1)), randn(10)) # issue #681
   
     # Non-differentiable sum of booleans
@@ -119,23 +120,15 @@ end
   
     @test gradcheck(x -> prod(x), (3,4))
     @test gradient(x -> prod(x), (1,2,3))[1] == (6,3,2)
-
-    # MethodError: no method matching copy(::Nothing)
-    @test_broken jacobicheck(x -> prod(x, dims = (2, 3)), (3,4,5))
+    @test jacobicheck(x -> prod(x, dims = (2, 3)), (3,4,5))
 end
   
 @testset "cumsum" begin
     @test jacobicheck(x -> cumsum(x), (4,))
-
-    # TypeError: in typeassert, expected Int64, got a value of type Nothing
-    @test_broken jacobicheck(x -> cumsum(x, dims=2), (3,4,5))
-    @test_broken jacobicheck(x -> cumsum(x, dims=3), (3,4)) # trivial
-
-    # MethodError: no method matching copy(::Nothing)
-    @test_broken jacobicheck(x -> cumsum(x, dims=1), (3,))
-
-    # Rewrite reached intrinsic function bitcast. Missing rule?
-    @test_broken jacobicheck(x -> cumsum(x, dims=3), (5,))  # trivial
+    @test jacobicheck(x -> cumsum(x, dims=2), (3,4,5))
+    @test jacobicheck(x -> cumsum(x, dims=3), (3,4)) # trivial
+    @test jacobicheck(x -> cumsum(x, dims=1), (3,))
+    @test jacobicheck(x -> cumsum(x, dims=3), (5,))  # trivial
 end
 
 @testset "getindex" begin
@@ -221,8 +214,7 @@ end
     @test jacobicheck(x -> reverse(x), rand(17))
     @test jacobicheck(x -> reverse(x, 8), rand(17))
     @test jacobicheck(x -> reverse(x, 8, 13), rand(17))
-    # Rewrite reached intrinsic function bitcast. Missing rule?
-    @test_broken jacobicheck(x -> reverse(x, dims=2), rand(17, 42))
+    @test jacobicheck(x -> reverse(x, dims=2), rand(17, 42))
 end
 
 @testset "permutedims" begin
@@ -237,11 +229,9 @@ end
 end
 
 @testset "repeat" begin
-    # MethodError: no method matching copy(::Nothing)
-    @test_broken jacobicheck(x -> repeat(x; inner=2), rand(5))
-    @test_broken jacobicheck(x -> repeat(x; inner=2, outer=3), rand(5))
-    @test_broken jacobicheck(x -> repeat(x; inner=(2,2,1), outer=(1,1,3)), rand(5,4,3))
-
+    @test jacobicheck(x -> repeat(x; inner=2), rand(5))
+    @test jacobicheck(x -> repeat(x; inner=2, outer=3), rand(5))
+    @test jacobicheck(x -> repeat(x; inner=(2,2,1), outer=(1,1,3)), rand(5,4,3))
     @test jacobicheck(x -> repeat(x, 3), rand(5))
     @test jacobicheck(x -> repeat(x, 2, 3), rand(5))
     @test jacobicheck(x -> repeat(x, 5), rand(5,7))
@@ -453,11 +443,10 @@ end
         @test gradient(v->sort(v)[i], [1.,2,3])[1][correct[2][i]] == 1
     end
     for i = 1:3
-        # Rewrite reached intrinsic function bitcast. Missing rule?
-        @test_broken gradient(v->sort(v,by=x->x%10)[i], [11,2,99])[1][correct[3][i]] == 1
-        @test_broken gradient(v->sort(v,by=x->x%10)[i], [2,11,99])[1][correct[4][i]] == 1
-        @test_broken gradient(v->sort(v,rev=true)[i], [3.,1,2])[1][correct[5][i]] == 1
-        @test_broken gradient(v->sort(v,rev=true)[i], [1.,2,3])[1][correct[6][i]] == 1
+        @test gradient(v->sort(v,by=x->x%10)[i], [11,2,99])[1][correct[3][i]] == 1
+        @test gradient(v->sort(v,by=x->x%10)[i], [2,11,99])[1][correct[4][i]] == 1
+        @test gradient(v->sort(v,rev=true)[i], [3.,1,2])[1][correct[5][i]] == 1
+        @test gradient(v->sort(v,rev=true)[i], [1.,2,3])[1][correct[6][i]] == 1
     end
 end
 
@@ -473,27 +462,21 @@ end
 
 @testset "maximum" begin
     @test jacobicheck(maximum, rand(2, 3))
-
-    # MethodError: no method matching copy(::Nothing)
-    @test_broken jacobicheck(x -> maximum(x, dims=1), rand(2, 3))
-    @test_broken jacobicheck(x -> maximum(x, dims=3), rand(2, 3, 4))
-    @test_broken jacobicheck(x -> maximum(x, dims=[1, 2]), rand(2, 3, 4))
-
+    @test jacobicheck(x -> maximum(x, dims=1), rand(2, 3))
+    @test jacobicheck(x -> maximum(x, dims=3), rand(2, 3, 4))
+    @test jacobicheck(x -> maximum(x, dims=[1, 2]), rand(2, 3, 4))
     @test gradient(x -> 1 / maximum(x), [1., 2, 3])[1] == [0, 0, -1/9]
 end
 
 @testset "minimum" begin
     @test jacobicheck(minimum, rand(2, 3))
-
-    # MethodError: no method matching copy(::Nothing)
-    @test_broken jacobicheck(x -> minimum(x, dims=1), rand(2, 3))
-    @test_broken jacobicheck(x -> minimum(x, dims=2), rand(2, 3))
+    @test jacobicheck(x -> minimum(x, dims=1), rand(2, 3))
+    @test jacobicheck(x -> minimum(x, dims=2), rand(2, 3))
 end
 
 @testset "dropdims" begin  # https://github.com/JuliaDiff/Diffractor.jl/issues/72
-    # TypeError: in typeassert, expected Int64, got a value of type Nothing
-    @test_broken jacobicheck(x -> dropdims(x, dims = 3), rand(2, 2, 1, 2))
-    @test_broken jacobicheck(x -> dropdims(x, dims = (2, 3)), rand(2, 1, 1, 3))
+    @test jacobicheck(x -> dropdims(x, dims = 3), rand(2, 2, 1, 2))
+    @test jacobicheck(x -> dropdims(x, dims = (2, 3)), rand(2, 1, 1, 3))
 end
 
 @testset "vcat" begin
@@ -544,20 +527,19 @@ end
 end
 
 @testset "cat(...; dims = $dim)" for dim in 1:3
-    # Rewrite reached intrinsic function bitcast. Missing rule?
 
     catdim = (x...) -> cat(x..., dims = dim)
-    @test_broken jacobicheck(catdim, rand(4,1))
-    @test_broken jacobicheck(catdim, rand(5), rand(5,1))
-    @test_broken jacobicheck(catdim, rand(2,5), rand(2,5), rand(2,5)) 
+    @test jacobicheck(catdim, rand(4,1))
+    @test jacobicheck(catdim, rand(5), rand(5,1))
+    @test jacobicheck(catdim, rand(2,5), rand(2,5), rand(2,5)) 
 
     catdimval = (x...) -> cat(x...; dims = Val(dim))
-    @test_broken jacobicheck(catdimval, rand(5), rand(5))
-    @test_broken jacobicheck(catdimval, rand(2,5), rand(2,5,1))
+    @test jacobicheck(catdimval, rand(5), rand(5))
+    @test jacobicheck(catdimval, rand(2,5), rand(2,5,1))
 
     # one empty
     dim == 1 || continue
-    @test_broken jacobicheck(catdim, rand(0,5,3), rand(2,5,3))
+    @test jacobicheck(catdim, rand(0,5,3), rand(2,5,3))
 end
 
 @testset "one(s) and zero(s)" begin
@@ -574,7 +556,7 @@ end
 end
 
 @testset "broadcast" begin
-    @test gradient(x -> sum(sin.(x)), Diagonal([0,pi/2,pi]))[1] ≈ [1 0 0; 0 0 0; 0 0 -1]
+    @test_broken gradient(x -> sum(sin.(x)), Diagonal([0,pi/2,pi]))[1] ≈ [1 0 0; 0 0 0; 0 0 -1]
 
     # mixing arrays & Ref(array)
     a = rand(3)
@@ -586,8 +568,7 @@ end
     # tests for https://github.com/FluxML/Zygote.jl/issues/724
     x1 = rand(3, 3)
     @test gradient(x -> sum(x .== 0.5), x1) |> only |> isZero
-    # MethodError: no method matching copy(::Nothing)
-    @test_broken gradient(x -> sum(x .* (x .== maximum(x, dims=1))), x1)[1] == (x1 .== maximum(x1, dims=1))
+    @test gradient(x -> sum(x .* (x .== maximum(x, dims=1))), x1)[1] == (x1 .== maximum(x1, dims=1))
 
     # tests for un-broadcasting *, / via scalar rules
     @test all(gradient((x,y) -> sum(x .* y), [1,2], 5) .≈ ([5, 5], 3))
@@ -620,7 +601,7 @@ end
     @test_broken jacobicheck(+, A, B, A)
     @test jacobicheck(-, A)
     # in typeassert, expected Int64, got a value of type Nothing
-    @test_broken jacobicheck(-, A, B)
+    @test jacobicheck(-, A, B)
 end
 
 end