diff --git a/base/promotion.jl b/base/promotion.jl
index 993f0be6c09242..b9ab5ed7254f79 100644
--- a/base/promotion.jl
+++ b/base/promotion.jl
@@ -172,7 +172,12 @@ function promote_typejoin(@nospecialize(a), @nospecialize(b))
     c = typejoin(_promote_typesubtract(a), _promote_typesubtract(b))
     return Union{a, b, c}::Type
 end
-_promote_typesubtract(@nospecialize(a)) = typesplit(a, Union{Nothing, Missing})
+_promote_typesubtract(@nospecialize(a)) =
+    a === Any ? a :
+    a >: Union{Nothing, Missing} ? typesplit(a, Union{Nothing, Missing}) :
+    a >: Nothing ? typesplit(a, Nothing) :
+    a >: Missing ? typesplit(a, Missing) :
+    a
 
 function promote_typejoin_union(::Type{T}) where T
     if T === Union{}
diff --git a/base/sort.jl b/base/sort.jl
index cbbcf948b8b4c7..1041c7e4288b34 100644
--- a/base/sort.jl
+++ b/base/sort.jl
@@ -578,19 +578,20 @@ elements that are not
 
 function _sort!(v::AbstractVector, a::MissingOptimization, o::Ordering, kw)
     @getkw lo hi
-    if nonmissingtype(eltype(v)) != eltype(v) && o isa DirectOrdering
+    if o isa DirectOrdering && eltype(v) >: Missing && nonmissingtype(eltype(v)) != eltype(v)
         lo, hi = send_to_end!(ismissing, v, o; lo, hi)
         _sort!(WithoutMissingVector(v, unsafe=true), a.next, o, (;kw..., lo, hi))
-    elseif eltype(v) <: Integer && o isa Perm && o.order isa DirectOrdering &&
-                nonmissingtype(eltype(o.data)) != eltype(o.data) &&
+    elseif o isa Perm && o.order isa DirectOrdering && eltype(v) <: Integer &&
+                eltype(o.data) >: Missing && nonmissingtype(eltype(o.data)) != eltype(o.data) &&
                 all(i === j for (i,j) in zip(v, eachindex(o.data)))
         # TODO make this branch known at compile time
         # This uses a custom function because we need to ensure stability of both sides and
         # we can assume v is equal to eachindex(o.data) which allows a copying partition
         # without allocations.
         lo_i, hi_i = lo, hi
-        for (i,x) in zip(eachindex(o.data), o.data)
-            if ismissing(x) == (o.order == Reverse) # should i go at the beginning?
+        for i in eachindex(o.data) # equal to copy(v)
+            x = o.data[i]
+            if ismissing(x) == (o.order == Reverse) # should x go at the beginning/end?
                 v[lo_i] = i
                 lo_i += 1
             else