diff --git a/base/promotion.jl b/base/promotion.jl
index af38a41118235..1ca5530a7b828 100644
--- a/base/promotion.jl
+++ b/base/promotion.jl
@@ -206,6 +206,7 @@ minmax(x::Real, y::Real) = minmax(promote(x, y)...)
 #   promote_op{R<:MyType,S<:MyType}(::typeof(*), ::Type{R}, ::Type{S}) = MyType{multype(R,S)}
 promote_op(::Any)    = (@_pure_meta; Bottom)
 promote_op(::Any, T) = (@_pure_meta; T)
+promote_op{T}(::Type{T}, ::Any) = (@_pure_meta; T)
 promote_op{R,S}(::Any, ::Type{R}, ::Type{S}) = (@_pure_meta; promote_type(R, S))
 promote_op(op, T, S, U, V...) = (@_pure_meta; promote_op(op, T, promote_op(op, S, U, V...)))
 
diff --git a/test/broadcast.jl b/test/broadcast.jl
index a3904ecc9a399..4bf1260b759e5 100644
--- a/test/broadcast.jl
+++ b/test/broadcast.jl
@@ -127,3 +127,8 @@ end
 let a = Real[2, 2.0, 4//2] / 2.0
     @test eltype(a) == Real
 end
+
+# issue 16164
+let a = broadcast(Float32, [3, 4, 5])
+    @test eltype(a) == Float32
+end