diff --git a/base/sort.jl b/base/sort.jl
index 1266da8a8c9df..669d2d97b2ac1 100644
--- a/base/sort.jl
+++ b/base/sort.jl
@@ -1560,8 +1560,14 @@ function sortperm(A::AbstractArray;
                   order::Ordering=Forward,
                   scratch::Union{Vector{<:Integer}, Nothing}=nothing,
                   dims...) #to optionally specify dims argument
-    ordr = ord(lt,by,rev,order)
-    if ordr === Forward && isa(A,Vector) && eltype(A)<:Integer
+    if rev === true
+        _sortperm(A; alg, order=ord(lt, by, true, order), scratch, dims...)
+    else
+        _sortperm(A; alg, order=ord(lt, by, nothing, order), scratch, dims...)
+    end
+end
+function _sortperm(A::AbstractArray; alg, order, scratch, dims...)
+    if order === Forward && isa(A,Vector) && eltype(A)<:Integer
         n = length(A)
         if n > 1
             min, max = extrema(A)
@@ -1573,7 +1579,7 @@ function sortperm(A::AbstractArray;
         end
     end
     ix = copymutable(LinearIndices(A))
-    sort!(ix; alg, order = Perm(ordr, vec(A)), scratch, dims...)
+    sort!(ix; alg, order = Perm(order, vec(A)), scratch, dims...)
 end
 
 
@@ -1615,7 +1621,7 @@ julia> sortperm!(p, A; dims=2); p
  2  4
 ```
 """
-function sortperm!(ix::AbstractArray{T}, A::AbstractArray;
+@inline function sortperm!(ix::AbstractArray{T}, A::AbstractArray;
                    alg::Algorithm=DEFAULT_UNSTABLE,
                    lt=isless,
                    by=identity,
@@ -1630,7 +1636,12 @@ function sortperm!(ix::AbstractArray{T}, A::AbstractArray;
     if !initialized
         ix .= LinearIndices(A)
     end
-    sort!(ix; alg, order = Perm(ord(lt, by, rev, order), vec(A)), scratch, dims...)
+
+    if rev === true
+        sort!(ix; alg, order=Perm(ord(lt, by, true, order), vec(A)), scratch, dims...)
+    else
+        sort!(ix; alg, order=Perm(ord(lt, by, nothing, order), vec(A)), scratch, dims...)
+    end
 end
 
 # sortperm for vectors of few unique integers
diff --git a/test/sorting.jl b/test/sorting.jl
index eb5020547c789..c4e324a61cde9 100644
--- a/test/sorting.jl
+++ b/test/sorting.jl
@@ -918,6 +918,28 @@ end
     @test bsqs()                            === bsqs(missing, missing, InsertionSort)
 end
 
+function test_allocs()
+    v = rand(10)
+    i = randperm(length(v))
+    @test 1 == @allocations sort(v)
+    @test 0 == @allocations sortperm!(i, v)
+    @test 0 == @allocations sort!(i)
+    @test 0 == @allocations sortperm!(i, v, rev=true)
+    @test 1 == @allocations sortperm(v, rev=true)
+    @test 1 == @allocations sortperm(v, rev=false)
+    @test 0 == @allocations sortperm!(i, v, order=Base.Reverse)
+    @test 1 == @allocations sortperm(v)
+    @test 1 == @allocations sortperm(i, by=sqrt)
+    @test 0 == @allocations sort!(v, lt=(a, b) -> hash(a) < hash(b))
+    sort!(Int[], rev=false) # compile
+    @test 0 == @allocations sort!(i, rev=false)
+    rand!(i)
+    @test 0 == @allocations sort!(i, order=Base.Reverse)
+end
+@testset "Small calls do not unnecessarily allocate" begin
+    test_allocs()
+end
+
 # This testset is at the end of the file because it is slow.
 @testset "searchsorted" begin
     numTypes = [ Int8,  Int16,  Int32,  Int64,  Int128,