diff --git a/src/SortingAlgorithms.jl b/src/SortingAlgorithms.jl
index e3df2f7..6b08cd1 100644
--- a/src/SortingAlgorithms.jl
+++ b/src/SortingAlgorithms.jl
@@ -16,12 +16,12 @@ struct TimSortAlg   <: Algorithm end
 struct RadixSortAlg <: Algorithm end
 struct CombSortAlg  <: Algorithm end
 
-function maybe_optimize(x::Algorithm) 
+function maybe_optimize(x::Algorithm)
     isdefined(Base.Sort, :InitialOptimizations) ? Base.Sort.InitialOptimizations(x) : x
-end     
+end
 const HeapSort  = maybe_optimize(HeapSortAlg())
 const TimSort   = maybe_optimize(TimSortAlg())
-# Whenever InitialOptimizations is defined, RadixSort falls 
+# Whenever InitialOptimizations is defined, RadixSort falls
 # back to Base.DEFAULT_STABLE which already includes them.
 const RadixSort = RadixSortAlg()
 
@@ -79,6 +79,27 @@ end
 #
 # Original author: @kmsquire
 
+@static if v"1.9.0-alpha" <= VERSION <= v"1.9.1"
+    function Base.getindex(v::Base.Sort.WithoutMissingVector, i::UnitRange)
+        out = Vector{eltype(v)}(undef, length(i))
+        out .= v.data[i]
+        out
+    end
+
+    # skip MissingOptimization due to JuliaLang/julia#50171
+    const _FIVE_ARG_SAFE_DEFAULT_STABLE = Base.DEFAULT_STABLE.next
+
+    # Explicitly define conversion from _sort!(v, alg, order, kw) to sort!(v, lo, hi, alg, order)
+    # To avoid excessively strict dispatch loop detection
+    function Base.Sort._sort!(v::AbstractVector, a::Union{HeapSortAlg, TimSortAlg, RadixSortAlg, CombSortAlg}, o::Base.Order.Ordering, kw)
+        Base.Sort.@getkw lo hi scratch
+        sort!(v, lo, hi, a, o)
+        scratch
+    end
+else
+    const _FIVE_ARG_SAFE_DEFAULT_STABLE = Base.DEFAULT_STABLE
+end
+
 const Run = UnitRange{Int}
 
 const MIN_GALLOP = 7
@@ -490,7 +511,7 @@ function sort!(v::AbstractVector, lo::Int, hi::Int, ::TimSortAlg, o::Ordering)
             # Make a run of length minrun
             count = min(minrun, hi-i+1)
             run_range = i:i+count-1
-            sort!(v, i, i+count-1, DEFAULT_STABLE, o)
+            sort!(v, i, i+count-1, _FIVE_ARG_SAFE_DEFAULT_STABLE, o)
         else
             if !issorted(run_range)
                 run_range = last(run_range):first(run_range)
diff --git a/test/runtests.jl b/test/runtests.jl
index 5738105..f8d9970 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -4,8 +4,9 @@ using StatsBase
 using Random
 
 a = rand(1:10000, 1000)
+am = [rand() < .9 ? i : missing for i in a]
 
-for alg in [TimSort, HeapSort, RadixSort, CombSort]
+for alg in [TimSort, HeapSort, RadixSort, CombSort, SortingAlgorithms.TimSortAlg()]
     b = sort(a, alg=alg)
     @test issorted(b)
     ix = sortperm(a, alg=alg)
@@ -13,6 +14,9 @@ for alg in [TimSort, HeapSort, RadixSort, CombSort]
     @test issorted(b)
     @test a[ix] == b
 
+    # legacy 3-argument calling convention
+    @test b == sort!(copy(a), alg, Base.Order.Forward)
+
     b = sort(a, alg=alg, rev=true)
     @test issorted(b, rev=true)
     ix = sortperm(a, alg=alg, rev=true)
@@ -34,9 +38,26 @@ for alg in [TimSort, HeapSort, RadixSort, CombSort]
     invpermute!(c, ix)
     @test c == a
 
-    if alg != RadixSort  # RadixSort does not work with Lt orderings
+    if alg != RadixSort  # RadixSort does not work with Lt orderings or missing
         c = sort(a, alg=alg, lt=(>))
         @test b == c
+
+        # Issue https://github.com/JuliaData/DataFrames.jl/issues/3340
+        bm1 = sort(am, alg=alg)
+        @test issorted(bm1)
+        @test count(ismissing, bm1) == count(ismissing, am)
+
+        bm2 = am[sortperm(am, alg=alg)]
+        @test issorted(bm2)
+        @test count(ismissing, bm2) == count(ismissing, am)
+
+        bm3 = am[sortperm!(collect(eachindex(am)), am, alg=alg)]
+        @test issorted(bm3)
+        @test count(ismissing, bm3) == count(ismissing, am)
+
+        if alg == TimSort # Stable
+            @test all(bm1 .=== bm2 .=== bm3)
+        end
     end
 
     c = sort(a, alg=alg, by=x->1/x)
@@ -103,8 +124,8 @@ for n in [0:10..., 100, 101, 1000, 1001]
         # test float sorting with NaNs
         s = sort(v, alg=alg, order=ord)
         @test issorted(s, order=ord)
-        
-        # This tests that NaNs (which compare equivalent) are treated stably 
+
+        # This tests that NaNs (which compare equivalent) are treated stably
         # even when the underlying algorithm is unstable. That it happens to
         # pass is not a part of the public API:
         @test reinterpret(UInt64, v[map(isnan, v)]) == reinterpret(UInt64, s[map(isnan, s)])