diff --git a/Project.toml b/Project.toml
index d0d3e60..317ff02 100644
--- a/Project.toml
+++ b/Project.toml
@@ -20,6 +20,7 @@ FillArraysStatisticsExt = "Statistics"
 
 [compat]
 Aqua = "0.8"
+Base64 = "1"
 Documenter = "1"
 Infinities = "0.1"
 LinearAlgebra = "1.6"
@@ -35,6 +36,7 @@ julia = "1.6"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+Base64 = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 Infinities = "e1ba4f0e-776d-440f-acd9-e1d2e9742647"
 PDMats = "90014a1f-27ba-587c-ab20-58faa44d9150"
@@ -47,4 +49,5 @@ Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "Test", "Infinities", "PDMats", "ReverseDiff", "SparseArrays", "StaticArrays", "Statistics", "Quaternions", "Documenter", "Random"]
+test = ["Aqua", "Base64", "Test", "Infinities", "PDMats", "ReverseDiff", "SparseArrays", "StaticArrays", "Statistics", "Quaternions", "Documenter", "Random"]
+
diff --git a/src/fillalgebra.jl b/src/fillalgebra.jl
index f98ae60..6b3d41d 100644
--- a/src/fillalgebra.jl
+++ b/src/fillalgebra.jl
@@ -18,14 +18,19 @@ for OP in (:transpose, :adjoint)
     end
 end
 
-permutedims(a::AbstractFillVector) = fillsimilar(a, (1, length(a)))
 permutedims(a::AbstractFillMatrix) = fillsimilar(a, reverse(axes(a)))
 
-function permutedims(B::AbstractFill, perm)
-    dimsB = size(B)
-    ndimsB = length(dimsB)
+@static if VERSION >= v"1.9"
+    Base.@constprop :aggressive permutedims(B::AbstractFill, perm) = _permutedims(B, perm)
+else
+    permutedims(B::AbstractFill, perm) = _permutedims(B, perm)
+end
+
+@inline function _permutedims(B::AbstractFill, perm)
+    dimsB = axes(B)
+    ndimsB = ndims(B)
     (ndimsB == length(perm) && isperm(perm)) || throw(ArgumentError("no valid permutation of dimensions"))
-    dimsP = ntuple(i->dimsB[perm[i]], ndimsB)::typeof(dimsB)
+    dimsP = ntuple(i->dimsB[perm[i]], ndimsB)
     fillsimilar(B, dimsP)
 end
 
diff --git a/test/runtests.jl b/test/runtests.jl
index 32cd2ed..a4b6871 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1488,17 +1488,17 @@ end
     @test Fill([1+im 2; 3 4; 5 6], 2,3)' == Fill([1+im 2; 3 4; 5 6]', 3,2)
     @test transpose(Fill([1+im 2; 3 4; 5 6], 2,3)) == Fill(transpose([1+im 2; 3 4; 5 6]), 3,2)
 
-    @test permutedims(Ones(10)) ≡ Ones(1,10)
-    @test permutedims(Zeros(10)) ≡ Zeros(1,10)
-    @test permutedims(Fill(2.0,10)) ≡ Fill(2.0,1,10)
-    @test permutedims(Ones(10,3)) ≡ Ones(3,10)
-    @test permutedims(Zeros(10,3)) ≡ Zeros(3,10)
-    @test permutedims(Fill(2.0,10,3)) ≡ Fill(2.0,3,10)
-
-    @test permutedims(Ones(2,4,5), [3,2,1]) == permutedims(Array(Ones(2,4,5)), [3,2,1])
-    @test permutedims(Ones(2,4,5), [3,2,1]) ≡ Ones(5,4,2)
-    @test permutedims(Zeros(2,4,5), [3,2,1]) ≡ Zeros(5,4,2)
-    @test permutedims(Fill(2.0,2,4,5), [3,2,1]) ≡ Fill(2.0,5,4,2)
+    @test @inferred(permutedims(Ones(10))) ≡ Ones(1,10)
+    @test @inferred(permutedims(Zeros(10))) ≡ Zeros(1,10)
+    @test @inferred(permutedims(Fill(2.0,10))) ≡ Fill(2.0,1,10)
+    @test @inferred(permutedims(Ones(10,3))) ≡ Ones(3,10)
+    @test @inferred(permutedims(Zeros(10,3))) ≡ Zeros(3,10)
+    @test @inferred(permutedims(Fill(2.0,10,3))) ≡ Fill(2.0,3,10)
+
+    @test @inferred(permutedims(Ones(2,4,5), [3,2,1])) == permutedims(Array(Ones(2,4,5)), [3,2,1])
+    @test @inferred(permutedims(Ones(2,4,5), [3,2,1])) ≡ Ones(5,4,2)
+    @test @inferred(permutedims(Zeros(2,4,5), [3,2,1])) ≡ Zeros(5,4,2)
+    @test @inferred(permutedims(Fill(2.0,2,4,5), [3,2,1])) ≡ Fill(2.0,5,4,2)
 
     @testset "recursive" begin
         S = SMatrix{2,3}(1:6)
@@ -1512,6 +1512,22 @@ end
         @test F' == G'
         @test transpose(F) == transpose(G)
     end
+
+    H = if VERSION >= v"1.8"
+        @inferred(permutedims(Fill(2, (SOneTo(2), SOneTo(3)))))
+    else
+        permutedims(Fill(2, (SOneTo(2), SOneTo(3))))
+    end
+    @test H === Fill(2, (SOneTo(3), SOneTo(2)))
+
+    # test for inference only if aggressive constant propagation is available
+    F = Fill(2, (SOneTo(2), SOneTo(3), SOneTo(1)))
+    H = if VERSION >= v"1.8"
+        @inferred((F -> permutedims(F, (3,1,2)))(F))
+    else
+        (F -> permutedims(F, (3,1,2)))(F)
+    end
+    @test H  === Fill(2, (SOneTo(1), SOneTo(2), SOneTo(3)))
 end
 
 @testset "reverse" begin