diff --git a/test/runtests.jl b/test/runtests.jl
index 88eaf976..51e76053 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -5,6 +5,8 @@ using Optimisers: @.., @lazy
 
 Random.seed!(1)
 
+# Fake "models" for testing
+
 struct Foo; x; y; end
 Functors.@functor Foo
 Optimisers.trainable(x::Foo) = (x.y, x.x)
@@ -16,6 +18,8 @@ Optimisers.trainable(x::TwoThirds) = (a = x.a,)
 mutable struct MutTwo; x; y; end
 Functors.@functor MutTwo
 
+# Simple rules for testing
+
 struct DummyHigherOrder <: AbstractRule end
 Optimisers.init(::DummyHigherOrder, x::AbstractArray) =
   (ones(eltype(x), size(x)), zero(x))
@@ -227,23 +231,6 @@ end
       @test_throws MethodError Optimisers.update(sm, m)
     end
 
-    @testset "2nd order gradient" begin
-      m = (α = ([1.0], sin), γ = Float32[4,3,2])
-
-      # Special rule which requires this:
-      s = Optimisers.setup(BiRule(), m)
-      g = (α = ([0.1], ZeroTangent()), γ = [1,10,100],)
-      s1, m1 = Optimisers.update(s, m, g, g)
-      @test m1.α[1] == [0.9]
-      @test_throws Exception Optimisers.update(s, m, g, map(x->2 .* x, g))
-
-      # Ordinary rule which doesn't need it:
-      s2 = Optimisers.setup(Adam(), m)
-      s3, m3 = Optimisers.update(s2, m, g)
-      s4, m4 = Optimisers.update(s2, m, g, g)
-      @test m3.γ == m4.γ
-    end
-
     @testset "broadcasting macros" begin
       x = [1.0, 2.0]; y = [3,4]; z = [5,6]
       @test (@lazy x + y * z) isa Broadcast.Broadcasted
@@ -365,34 +352,53 @@ end
          @test model2.a === model2.b  # tie of MutTwo structs is restored
          @test model2.a !== model2.c  # but a new tie is not created
       end
-    end
+    end  # tied weights
+
+    @testset "2nd-order interface" begin
+      @testset "BiRule" begin
+        m = (α = ([1.0], sin), γ = Float32[4,3,2])
+
+        # Special rule which requires this:
+        s = Optimisers.setup(BiRule(), m)
+        g = (α = ([0.1], ZeroTangent()), γ = [1,10,100],)
+        s1, m1 = Optimisers.update(s, m, g, g)
+        @test m1.α[1] == [0.9]
+        @test_throws Exception Optimisers.update(s, m, g, map(x->2 .* x, g))
+
+        # Ordinary rule which doesn't need it:
+        s2 = Optimisers.setup(Adam(), m)
+        s3, m3 = Optimisers.update(s2, m, g)
+        s4, m4 = Optimisers.update(s2, m, g, g)
+        @test m3.γ == m4.γ
+      end
 
-    @testset "higher order interface" begin
-      w, b = rand(3, 4), rand(3)
-
-      o = DummyHigherOrder()
-      psin = (w, b)
-      dxs = map(x -> rand(size(x)...), psin)
-      dx2s = map(x -> rand(size(x)...), psin)
-      stin = Optimisers.setup(o, psin)
-      stout, psout = Optimisers.update(stin, psin, dxs, dx2s)
-
-      # hardcoded rule behavior for dummy rule
-      @test psout[1] == dummy_update_rule(stin[1].state, psin[1], dxs[1], dx2s[1])
-      @test psout[2] == dummy_update_rule(stin[2].state, psin[2], dxs[2], dx2s[2])
-      @test stout[1].state[1] == stin[1].state[1] .+ 1
-      @test stout[2].state[2] == stin[2].state[2] .+ 1
-
-      # error if only given one derivative
-      @test_throws MethodError Optimisers.update(stin, psin, dxs)
-
-      # first-order rules compose with second-order
-      ochain = OptimiserChain(Descent(0.1), o)
-      stin = Optimisers.setup(ochain, psin)
-      stout, psout = Optimisers.update(stin, psin, dxs, dx2s)
-      @test psout[1] == dummy_update_rule(stin[1].state[2], psin[1], 0.1 * dxs[1], dx2s[1])
-      @test psout[2] == dummy_update_rule(stin[2].state[2], psin[2], 0.1 * dxs[2], dx2s[2])
-    end
+      @testset "DummyHigherOrder" begin
+        w, b = rand(3, 4), rand(3)
+
+        o = DummyHigherOrder()
+        psin = (w, b)
+        dxs = map(x -> rand(size(x)...), psin)
+        dx2s = map(x -> rand(size(x)...), psin)
+        stin = Optimisers.setup(o, psin)
+        stout, psout = Optimisers.update(stin, psin, dxs, dx2s)
+
+        # hardcoded rule behavior for dummy rule
+        @test psout[1] == dummy_update_rule(stin[1].state, psin[1], dxs[1], dx2s[1])
+        @test psout[2] == dummy_update_rule(stin[2].state, psin[2], dxs[2], dx2s[2])
+        @test stout[1].state[1] == stin[1].state[1] .+ 1
+        @test stout[2].state[2] == stin[2].state[2] .+ 1
+
+        # error if only given one derivative
+        @test_throws MethodError Optimisers.update(stin, psin, dxs)
+
+        # first-order rules compose with second-order
+        ochain = OptimiserChain(Descent(0.1), o)
+        stin = Optimisers.setup(ochain, psin)
+        stout, psout = Optimisers.update(stin, psin, dxs, dx2s)
+        @test psout[1] == dummy_update_rule(stin[1].state[2], psin[1], 0.1 * dxs[1], dx2s[1])
+        @test psout[2] == dummy_update_rule(stin[2].state[2], psin[2], 0.1 * dxs[2], dx2s[2])
+      end
+    end  # 2nd-order
 
   end
   @testset verbose=true "Destructure" begin