diff --git a/Project.toml b/Project.toml
index 18d60250..80959f00 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "Bijectors"
 uuid = "76274a88-744f-5084-9051-94815aaf08c4"
-version = "0.13.7"
+version = "0.13.8"
 
 [deps]
 ArgCheck = "dce04be8-c92d-5529-be00-80e4d2c0e197"
diff --git a/src/interface.jl b/src/interface.jl
index 8d401e5a..1ba9aa60 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -42,6 +42,7 @@ with_logabsdet_jacobian(f::Columnwise, x::AbstractMatrix) = (f(x), logabsdetjac(
 Returns the output size of `f` given the input size `sz`.
 """
 output_size(f, sz) = sz
+output_size(f::ComposedFunction, sz) = output_size(f.outer, output_size(f.inner, sz))
 
 """
     output_length(f, len::Int)
diff --git a/test/bijectors/stacked.jl b/test/bijectors/stacked.jl
index 655b63eb..1f221b39 100644
--- a/test/bijectors/stacked.jl
+++ b/test/bijectors/stacked.jl
@@ -34,4 +34,44 @@ end
         @test y == [exp(1.0), 2.0]
         @test binv(y) == [1.0, 2.0, 0.0]
     end
+
+    @testset "composition" begin
+        # Composition with one dimension reduction.
+        b = Stacked((elementwise(exp), ProjectionBijector() ∘ identity), [1:1, 2:3])
+        binv = inverse(b)
+        x = [1.0, 2.0, 3.0]
+        y = b(x)
+        x_ = binv(y)
+
+        # Are the values of correct size?
+        @test size(y) == (2,)
+        @test size(x_) == (3,)
+        # Can we determine the sizes correctly?
+        @test Bijectors.output_size(b, size(x)) == (2,)
+        @test Bijectors.output_size(binv, size(y)) == (3,)
+
+        # Are values correct?
+        @test y == [exp(1.0), 2.0]
+        @test binv(y) == [1.0, 2.0, 0.0]
+
+        # Composition with two dimension reductions.
+        b = Stacked(
+            (elementwise(exp), ProjectionBijector() ∘ ProjectionBijector()), [1:1, 2:4]
+        )
+        binv = inverse(b)
+        x = [1.0, 2.0, 3.0, 4.0]
+        y = b(x)
+        x_ = binv(y)
+
+        # Are the values of correct size?
+        @test size(y) == (2,)
+        @test size(x_) == (4,)
+        # Can we determine the sizes correctly?
+        @test Bijectors.output_size(b, size(x)) == (2,)
+        @test Bijectors.output_size(binv, size(y)) == (4,)
+
+        # Are values correct?
+        @test y == [exp(1.0), 2.0]
+        @test binv(y) == [1.0, 2.0, 0.0, 0.0]
+    end
 end