diff --git a/base/array.jl b/base/array.jl
index 083e4a4323f7f6..22c6b272005efb 100644
--- a/base/array.jl
+++ b/base/array.jl
@@ -561,7 +561,7 @@ function collect_to!(dest::AbstractArray{T}, itr, offs, st) where T
             @inbounds dest[i] = el::T
             i += 1
         else
-            R = typejoin(T, S)
+            R = promote_join(T, S)
             new = similar(dest, R)
             copy!(new,1, dest,1, i-1)
             @inbounds new[i] = el
@@ -584,7 +584,7 @@ function grow_to!(dest, itr, st)
         if S === T || S <: T
             push!(dest, el::T)
         else
-            new = similar(dest, typejoin(T, S))
+            new = similar(dest, promote_join(T, S))
             copy!(new, dest)
             push!(new, el)
             return grow_to!(new, itr, st)
diff --git a/base/broadcast.jl b/base/broadcast.jl
index 7168971c2ac316..ddf51d4e523e09 100644
--- a/base/broadcast.jl
+++ b/base/broadcast.jl
@@ -487,7 +487,7 @@ end
             else
                 # This element type doesn't fit in B. Allocate a new B with wider eltype,
                 # copy over old values, and continue
-                newB = Base.similar(B, typejoin(eltype(B), S))
+                newB = Base.similar(B, promote_join(eltype(B), S))
                 for II in Iterators.take(iter, count)
                     newB[II] = B[II]
                 end
diff --git a/base/dict.jl b/base/dict.jl
index bd3ac41287e550..ca66d780a182ff 100644
--- a/base/dict.jl
+++ b/base/dict.jl
@@ -179,7 +179,7 @@ function grow_to!(dest::Associative{K,V}, itr, st) where V where K
         if isa(k,K) && isa(v,V)
             dest[k] = v
         else
-            new = empty(dest, typejoin(K,typeof(k)), typejoin(V,typeof(v)))
+            new = empty(dest, promote_join(K,typeof(k)), promote_join(V,typeof(v)))
             copy!(new, dest)
             new[k] = v
             return grow_to!(new, itr, st)
diff --git a/base/inference.jl b/base/inference.jl
index 6b5f867eabf7f1..2df71055660aa9 100644
--- a/base/inference.jl
+++ b/base/inference.jl
@@ -1833,7 +1833,7 @@ function limit_tuple_type_n(@nospecialize(t), lim::Int)
     p = t.parameters
     n = length(p)
     if n > lim
-        tail = reduce(typejoin, Bottom, Any[p[lim:(n-1)]..., unwrapva(p[n])])
+        tail = reduce(promote_join, Bottom, Any[p[lim:(n-1)]..., unwrapva(p[n])])
         return Tuple{p[1:(lim-1)]..., Vararg{tail}}
     end
     return t
diff --git a/base/promotion.jl b/base/promotion.jl
index 89a479d8a5af70..64ceee529f285b 100644
--- a/base/promotion.jl
+++ b/base/promotion.jl
@@ -2,17 +2,11 @@
 
 ## type join (closest common ancestor, or least upper bound) ##
 
-# Note: no methods must be added to this function after `typejoin` has been defined,
-# since it is declared as `@pure`
-isspecial(::Type) = false
-isspecial(::Type{Void}) = true
-isspecial(::Type{Missing}) = true
-isspecialpair(a, b) = isconcrete(a) && isconcrete(b) && (isspecial(a) || isspecial(b))
-
 """
     typejoin(T, S)
 
-Compute a type that contains both `T` and `S`.
+Return the closest common ancestor of `T` and `S`, i.e. a type which
+contains both of them.
 """
 typejoin() = (@_pure_meta; Bottom)
 typejoin(@nospecialize(t)) = (@_pure_meta; t)
@@ -31,9 +25,9 @@ function typejoin(@nospecialize(a), @nospecialize(b))
         return typejoin(a.ub, b)
     elseif isa(b,TypeVar)
         return typejoin(a, b.ub)
-    elseif isa(a,Union) && !isspecialpair(a.a, a.b)
+    elseif isa(a,Union)
         return typejoin(typejoin(a.a,a.b), b)
-    elseif isa(b,Union) && !isspecialpair(b.a, b.b)
+    elseif isa(b,Union)
         return typejoin(a, typejoin(b.a,b.b))
     elseif a <: Tuple
         if !(b <: Tuple)
@@ -82,10 +76,9 @@ function typejoin(@nospecialize(a), @nospecialize(b))
     elseif b <: Tuple
         return Any
     end
-    b2 = b
-    while b2 !== Any && a isa DataType && b2 isa DataType
-        if a <: b2.name.wrapper
-            while a.name !== b2.name
+    while b !== Any
+        if a <: b.name.wrapper
+            while a.name !== b.name
                 a = supertype(a)
             end
             aprimary = unwrap_unionall(a.name.wrapper)
@@ -96,7 +89,7 @@ function typejoin(@nospecialize(a), @nospecialize(b))
             end
             p = Vector{Any}(uninitialized, n)
             for i = 1:n
-                ai, bi = a.parameters[i], b2.parameters[i]
+                ai, bi = a.parameters[i], b.parameters[i]
                 if ai === bi || (isa(ai,Type) && isa(bi,Type) && typeseq(ai,bi))
                     p[i] = ai
                 else
@@ -105,12 +98,30 @@ function typejoin(@nospecialize(a), @nospecialize(b))
             end
             return rewrap_unionall(a.name.wrapper{p...}, a.name.wrapper)
         end
-        b2 = supertype(b2)
+        b = supertype(b)
     end
-    isspecialpair(a, b) && return Union{a, b}
     return Any
 end
 
+"""
+    promote_join(T, S)
+
+Compute a type that contains both `T` and `S`, which could be
+either a parent of both types, or a `Union` if appropriate.
+Falls back to [`typejoin`](@ref).
+"""
+promote_join(@nospecialize(a), @nospecialize(b)) = typejoin(a, b)
+promote_join(::Type{Void}, ::Type{T}) where {T} =
+    isconcrete(T) ? Union{T, Void} : Any
+promote_join(::Type{T}, ::Type{Void}) where {T} =
+    isconcrete(T) ? Union{T, Void} : Any
+promote_join(::Type{Missing}, ::Type{T}) where {T} =
+    isconcrete(T) ? Union{T, Missing} : Any
+promote_join(::Type{T}, ::Type{Missing}) where {T} =
+    isconcrete(T) ? Union{T, Missing} : Any
+promote_join(::Type{Void}, ::Type{Missing}) = Union{Void, Missing}
+promote_join(::Type{Missing}, ::Type{Void}) = Union{Void, Missing}
+
 # Returns length, isfixed
 function full_va_len(p)
     isempty(p) && return 0, true
diff --git a/base/range.jl b/base/range.jl
index 3615a99a2d257f..2169f0b88f8aee 100644
--- a/base/range.jl
+++ b/base/range.jl
@@ -807,7 +807,7 @@ broadcast(::typeof(\), x::Number, r::LinSpace)      = LinSpace(x \ r.start, x \
 el_same(::Type{T}, a::Type{<:AbstractArray{T,n}}, b::Type{<:AbstractArray{T,n}}) where {T,n}   = a
 el_same(::Type{T}, a::Type{<:AbstractArray{T,n}}, b::Type{<:AbstractArray{S,n}}) where {T,S,n} = a
 el_same(::Type{T}, a::Type{<:AbstractArray{S,n}}, b::Type{<:AbstractArray{T,n}}) where {T,S,n} = b
-el_same(::Type, a, b) = typejoin(a, b)
+el_same(::Type, a, b) = promote_join(a, b)
 
 promote_rule(a::Type{UnitRange{T1}}, b::Type{UnitRange{T2}}) where {T1,T2} =
     el_same(promote_type(T1,T2), a, b)
diff --git a/base/set.jl b/base/set.jl
index dea43bc4b665f3..79381a18c8bb4d 100644
--- a/base/set.jl
+++ b/base/set.jl
@@ -128,7 +128,7 @@ function union!(s::Set{T}, xs) where T
 end
 
 join_eltype() = Bottom
-join_eltype(v1, vs...) = typejoin(eltype(v1), join_eltype(vs...))
+join_eltype(v1, vs...) = promote_join(eltype(v1), join_eltype(vs...))
 
 """
     intersect(s1,s2...)
@@ -278,7 +278,7 @@ _unique_from(itr, out, seen, i) = unique_from(itr, out, seen, i)
         x, i = next(itr, i)
         S = typeof(x)
         if !(S === T || S <: T)
-            R = typejoin(S, T)
+            R = promote_join(S, T)
             seenR = convert(Set{R}, seen)
             outR = convert(Vector{R}, out)
             if !in(x, seenR)
diff --git a/base/tuple.jl b/base/tuple.jl
index 2b94d1d946e44e..7bb22c0cf27912 100644
--- a/base/tuple.jl
+++ b/base/tuple.jl
@@ -78,11 +78,11 @@ end
 eltype(t::Type{<:Tuple}) = _compute_eltype(t)
 function _compute_eltype(t::Type{<:Tuple})
     @_pure_meta
-    t isa Union && return typejoin(eltype(t.a), eltype(t.b))
+    t isa Union && return promote_join(eltype(t.a), eltype(t.b))
     t´ = unwrap_unionall(t)
     r = Union{}
     for ti in t´.parameters
-        r = typejoin(r, rewrap_unionall(unwrapva(ti), t))
+        r = promote_join(r, rewrap_unionall(unwrapva(ti), t))
     end
     return r
 end
diff --git a/test/core.jl b/test/core.jl
index 7ccd05692043cc..5f486d62d28658 100644
--- a/test/core.jl
+++ b/test/core.jl
@@ -123,17 +123,17 @@ end
 @test typejoin(Tuple{Vararg{Int,2}}, Tuple{Int,Int,Int}) === Tuple{Int,Int,Vararg{Int}}
 @test typejoin(Tuple{Vararg{Int,2}}, Tuple{Vararg{Int}}) === Tuple{Vararg{Int}}
 
-# typejoin returns a Union only with Void/Missing combined with concrete types
+# promote_join returns a Union only with Void/Missing combined with concrete types
 for T in (Void, Missing)
-    @test typejoin(Int, Float64) === Real
-    @test typejoin(Int, T) === Union{Int, T}
-    @test typejoin(T, String) === Union{T, String}
-    @test typejoin(Vector{Int}, T) === Union{Vector{Int}, T}
-    @test typejoin(Vector, T) === Any
-    @test typejoin(Real, T) === Any
-    @test typejoin(Int, String) === Any
-    @test typejoin(Int, Union{Float64, T}) === Any
-    @test typejoin(Int, Union{String, T}) === Any
+    @test Base.promote_join(Int, Float64) === Real
+    @test Base.promote_join(Int, T) === Union{Int, T}
+    @test Base.promote_join(T, String) === Union{T, String}
+    @test Base.promote_join(Vector{Int}, T) === Union{Vector{Int}, T}
+    @test Base.promote_join(Vector, T) === Any
+    @test Base.promote_join(Real, T) === Any
+    @test Base.promote_join(Int, String) === Any
+    @test Base.promote_join(Int, Union{Float64, T}) === Any
+    @test Base.promote_join(Int, Union{String, T}) === Any
 end
 
 @test promote_type(Bool,Bottom) === Bool