diff --git a/Project.toml b/Project.toml
index 9d89ca821..91a7b526e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRulesCore"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.15.5"
+version = "1.15.6"
 
 [deps]
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
diff --git a/src/tangent_types/notimplemented.jl b/src/tangent_types/notimplemented.jl
index 661308a11..7016acd60 100644
--- a/src/tangent_types/notimplemented.jl
+++ b/src/tangent_types/notimplemented.jl
@@ -43,6 +43,11 @@ Base.:/(x::NotImplemented, ::Any) = throw(NotImplementedException(x))
 Base.:/(::Any, x::NotImplemented) = throw(NotImplementedException(x))
 Base.:/(x::NotImplemented, ::NotImplemented) = throw(NotImplementedException(x))
 
+# Fix method ambiguity errors (#589)
+Base.:/(x::AbstractZero, ::NotImplemented) = x
+Base.:/(x::NotImplemented, ::AbstractThunk) = throw(NotImplementedException(x))
+Base.:/(::AbstractThunk, x::NotImplemented) = throw(NotImplementedException(x))
+
 Base.zero(x::NotImplemented) = throw(NotImplementedException(x))
 function Base.zero(::Type{<:NotImplemented})
     return throw(
diff --git a/src/tangent_types/thunks.jl b/src/tangent_types/thunks.jl
index 8baa006e8..3af284671 100644
--- a/src/tangent_types/thunks.jl
+++ b/src/tangent_types/thunks.jl
@@ -33,8 +33,13 @@ Base.:(==)(a::AbstractThunk, b::AbstractThunk) = unthunk(a) == unthunk(b)
 Base.:(-)(a::AbstractThunk) = -unthunk(a)
 Base.:(-)(a::AbstractThunk, b) = unthunk(a) - b
 Base.:(-)(a, b::AbstractThunk) = a - unthunk(b)
+Base.:(-)(a::AbstractThunk, b::AbstractThunk) = unthunk(a) - unthunk(b)
 Base.:(/)(a::AbstractThunk, b) = unthunk(a) / b
 Base.:(/)(a, b::AbstractThunk) = a / unthunk(b)
+Base.:(/)(a::AbstractThunk, b::AbstractThunk) = unthunk(a) / unthunk(b)
+
+# Fix method ambiguity issue
+Base.:/(a::AbstractZero, ::AbstractThunk) = a
 
 Base.real(a::AbstractThunk) = real(unthunk(a))
 Base.imag(a::AbstractThunk) = imag(unthunk(a))
diff --git a/test/tangent_types/notimplemented.jl b/test/tangent_types/notimplemented.jl
index ea460dfd5..e113475c1 100644
--- a/test/tangent_types/notimplemented.jl
+++ b/test/tangent_types/notimplemented.jl
@@ -21,7 +21,7 @@
         @test ni + ni2 === ni
         @test ni2 + ni === ni2
 
-        # multiplication and dot product
+        # multiplication, division, and dot product
         @test -ni == ni
         for a in (true, x, thunk)
             @test ni * a === ni
@@ -32,6 +32,7 @@
         for a in (NoTangent(), ZeroTangent())
             @test ni * a === a
             @test a * ni === a
+            @test a / ni === a
             @test dot(ni, a) === a
             @test dot(a, ni) === a
         end
@@ -52,8 +53,10 @@
             @test_throws E a - ni
         end
         @test_throws E ni - ni2
-        @test_throws E ni / x
-        @test_throws E x / ni
+        for a in (true, x, thunk)
+            @test_throws E ni / a
+            @test_throws E a / ni
+        end
         @test_throws E ni / ni2
         @test_throws E zero(ni)
         @test_throws E zero(typeof(ni))
diff --git a/test/tangent_types/thunks.jl b/test/tangent_types/thunks.jl
index 68c2cc53a..c799e5c09 100644
--- a/test/tangent_types/thunks.jl
+++ b/test/tangent_types/thunks.jl
@@ -101,8 +101,15 @@
         @test 1 == -@thunk(-1)
         @test 1 == @thunk(2) - 1
         @test 1 == 2 - @thunk(1)
+        @test 1 == @thunk(2) - @thunk(1)
         @test 1.0 == @thunk(1) / 1.0
         @test 1.0 == 1.0 / @thunk(1)
+        @test 1 == @thunk(1) / @thunk(1)
+
+        # check method ambiguities (#589)
+        for a in (ZeroTangent(), NoTangent())
+            @test a / @thunk(2) === a
+        end
 
         @test 1 == real(@thunk(1 + 1im))
         @test 1 == imag(@thunk(1 + 1im))