diff --git a/src/projection.jl b/src/projection.jl
index 8eba26353..811802536 100644
--- a/src/projection.jl
+++ b/src/projection.jl
@@ -283,7 +283,11 @@ end
 (project::ProjectTo{<:Tangent{<:Ref}})(dx::Tangent) = project(Ref(first(backing(dx))))
 function (project::ProjectTo{<:Tangent{<:Ref}})(dx::Ref)
     dy = project.x(dx[])
-    return project_type(project)(; x=dy)
+    if dy isa AbstractZero
+        return NoTangent()
+    else
+        return project_type(project)(; x=dy)
+    end
 end
 # Since this works like a zero-array in broadcasting, it should also accept a number:
 (project::ProjectTo{<:Tangent{<:Ref}})(dx::Number) = project(Ref(dx))
@@ -321,7 +325,11 @@ function (project::ProjectTo{<:Tangent{<:Tuple}})(dx::Tuple)
     end
     # Here map will fail if the lengths don't match, but gives a much less helpful error:
     dy = map((f, x) -> f(x), project.elements, dx)
-    return project_type(project)(dy...)
+    if all(d -> d isa AbstractZero, dy)
+        return NoTangent()
+    else
+        return project_type(project)(dy...)
+    end
 end
 function (project::ProjectTo{<:Tangent{<:NamedTuple}})(dx::NamedTuple)
     dy = _project_namedtuple(backing(project), dx)
@@ -370,7 +378,11 @@ function (project::ProjectTo{<:Tangent{<:Tuple}})(dx::AbstractArray)
     end
     dy = reshape(dx, axes(project.elements))  # allows for dx::OffsetArray
     dz = ntuple(i -> project.elements[i](dy[i]), length(project.elements))
-    return project_type(project)(dz...)
+    if all(d -> d isa AbstractZero, dy)
+        return NoTangent()
+    else
+        return project_type(project)(dz...)
+    end
 end
 
 
diff --git a/test/projection.jl b/test/projection.jl
index 3e70772ac..d6a8633bb 100644
--- a/test/projection.jl
+++ b/test/projection.jl
@@ -143,16 +143,19 @@ struct NoSuperType end
 
         @test ProjectTo(Ref(true)) isa ProjectTo{NoTangent}
         @test ProjectTo(Ref([false]')) isa ProjectTo{NoTangent}
+        
+        @test ProjectTo(Ref(1.0))(Ref(NoTangent())) === NoTangent()  # collapse all-zero
     end
 
     @testset "Base: Tuple" begin
         pt1 = ProjectTo((1.0,))
-        @test pt1((1 + im,)) == Tangent{Tuple{Float64}}(1.0,)
-        @test pt1(pt1((1,))) == pt1(pt1((1,)))            # accepts correct Tangent
-        @test pt1(Tangent{Any}(1)) == pt1((1,))           # accepts Tangent{Any}
+        @test @inferred(pt1((1 + im,))) == Tangent{Tuple{Float64}}(1.0,)
+        @test @inferred(pt1(pt1((1,)))) == pt1(pt1((1,)))            # accepts correct Tangent
+        @test @inferred(pt1(Tangent{Any}(1))) == pt1((1,))           # accepts Tangent{Any}
         @test pt1([1,]) == Tangent{Tuple{Float64}}(1.0,)  # accepts Vector
-        @test pt1(NoTangent()) === NoTangent()
-        @test pt1(ZeroTangent()) === ZeroTangent()
+        @test @inferred(pt1(NoTangent())) === NoTangent()
+        @test @inferred(pt1(ZeroTangent())) === ZeroTangent()
+        @test @inferred(pt1((NoTangent(),))) === NoTangent()  # collapse all-zero
 
         @test_throws Exception pt1([1, 2]) # DimensionMismatch, wrong length
         @test_throws Exception pt1([])