diff --git a/test/spaces.jl b/test/spaces.jl
index b37b3b7b..4039c429 100644
--- a/test/spaces.jl
+++ b/test/spaces.jl
@@ -279,6 +279,7 @@ println("------------------------------------")
         @test @constinferred(⊗(V1, V2, V3 ⊗ V4)) == P
         @test @constinferred(⊗(V1, V2 ⊗ V3, V4)) == P
         @test @constinferred(insertunit(P, 3)) == V1 * V2 * oneunit(V1) * V3 * V4
+        @test @constinferred(removeunit(V1 * V2 * oneunit(V1)' * V3 * V4, 3)) == P
         @test fuse(V1, V2', V3) ≅ V1 ⊗ V2' ⊗ V3
         @test fuse(V1, V2', V3) ≾ V1 ⊗ V2' ⊗ V3
         @test fuse(V1, V2', V3) ≿ V1 ⊗ V2' ⊗ V3
@@ -339,6 +340,7 @@ println("------------------------------------")
         @test @constinferred(⊗(V1, V2, V3)) == P
         @test @constinferred(adjoint(P)) == dual(P) == V3' ⊗ V2' ⊗ V1'
         @test @constinferred(insertunit(P, 3; conj=true)) == V1 * V2 * oneunit(V1)' * V3
+        @test P == @constinferred(removeunit(insertunit(P, 3), 3))
         @test fuse(V1, V2', V3) ≅ V1 ⊗ V2' ⊗ V3
         @test fuse(V1, V2', V3) ≾ V1 ⊗ V2' ⊗ V3 ≾ fuse(V1 ⊗ V2' ⊗ V3)
         @test fuse(V1, V2') ⊗ V3 ≾ V1 ⊗ V2' ⊗ V3
@@ -420,11 +422,14 @@ println("------------------------------------")
         @test permute(W, ((2, 4, 5), (3, 1))) == (V2 ⊗ V4' ⊗ V5' ← V3 ⊗ V1')
         @test (V1 ⊗ V2 ← V1 ⊗ V2) == @constinferred TensorKit.compose(W, W')
         @test @constinferred(insertunit(W)) == (V1 ⊗ V2 ← V3 ⊗ V4 ⊗ V5 ⊗ oneunit(V5))
+        @test @constinferred(removeunit(insertunit(W), numind(W) + 1)) == W
         @test @constinferred(insertunit(W; conj=true)) == (V1 ⊗ V2 ←
                                                            V3 ⊗ V4 ⊗ V5 ⊗ oneunit(V5)')
         @test @constinferred(insertunit(W, 1)) == (oneunit(V1) ⊗ V1 ⊗ V2 ← V3 ⊗ V4 ⊗ V5)
         @test @constinferred(insertunit(W, 3)) == (V1 ⊗ V2 ⊗ oneunit(V1) ← V3 ⊗ V4 ⊗ V5)
+        @test @constinferred(removeunit(insertunit(W, 3))) == W
         @test @constinferred(insertunit(W, 3; preferdomain=true)) ==
               (V1 ⊗ V2 ← oneunit(V1) ⊗ V3 ⊗ V4 ⊗ V5)
+        @test @constinferred(removeunit(insertunit(W, 3; preferdomain=true), 3)) == W
     end
 end
diff --git a/test/tensors.jl b/test/tensors.jl
index 18d9aba2..15ea076e 100644
--- a/test/tensors.jl
+++ b/test/tensors.jl
@@ -182,21 +182,25 @@ for V in spacelist
                 @test space(t2) == insertunit(space(t))
                 @test scalartype(t2) === T
                 @test t.data === t2.data
+                @test @constinferred(removeunit(t2, numind(t2))) == t
                 t3 = @constinferred insertunit(t; copy=true)
                 @test t.data !== t3.data
                 for (c, b) in blocks(t)
                     @test b == block(t3, c)
                 end
+                @test @constinferred(removeunit(t3, numind(t3))) == t
                 t4 = @constinferred insertunit(t, 4; dual=true)
                 @test numin(t4) == numin(t) && numout(t4) == numout(t) + 1
                 for (c, b) in blocks(t)
                     @test b == block(t4, c)
                 end
+                @test @constinferred(removeunit(t4, 4)) == t
                 t5 = @constinferred insertunit(t, 4; dual=true)
                 @test numin(t5) == numin(t) + 1 && numout(t5) == numout(t)
                 for (c, b) in blocks(t)
                     @test b == block(t5, c)
                 end
+                @test @constinferred(removeunit(t5, 4)) == t
             end
         end
         if hasfusiontensor(I)