diff --git a/base/essentials.jl b/base/essentials.jl
index 35a52e592434e..575d3aac0e9d0 100644
--- a/base/essentials.jl
+++ b/base/essentials.jl
@@ -264,11 +264,22 @@ function typename(a::Union)
 end
 typename(union::UnionAll) = typename(union.body)
 
-convert(::Type{T}, x::T) where {T<:Tuple{Any, Vararg{Any}}} = x
-convert(::Type{Tuple{}}, x::Tuple{Any, Vararg{Any}}) = throw(MethodError(convert, (Tuple{}, x)))
-convert(::Type{T}, x::Tuple{Any, Vararg{Any}}) where {T<:Tuple} =
+const AtLeast1 = Tuple{Any, Vararg{Any}}
+
+# converting to empty tuple type
+convert(::Type{Tuple{}}, ::Tuple{}) = ()
+convert(::Type{Tuple{}}, x::AtLeast1) = throw(MethodError(convert, (Tuple{}, x)))
+
+# converting to tuple types with at least one element
+convert(::Type{T}, x::T) where {T<:AtLeast1} = x
+convert(::Type{T}, x::AtLeast1) where {T<:AtLeast1} =
     (convert(tuple_type_head(T), x[1]), convert(tuple_type_tail(T), tail(x))...)
 
+# converting to Vararg tuple types
+convert(::Type{Tuple{Vararg{V}}}, x::Tuple{Vararg{V}}) where {V} = x
+convert(T::Type{Tuple{Vararg{V}}}, x::Tuple) where {V} =
+    (convert(tuple_type_head(T), x[1]), convert(T, tail(x))...)
+
 # TODO: the following definitions are equivalent (behaviorally) to the above method
 # I think they may be faster / more efficient for inference,
 # if we could enable them, but are they?
diff --git a/test/ambiguous.jl b/test/ambiguous.jl
index 6835a2c1977f7..02d076d5eb8ba 100644
--- a/test/ambiguous.jl
+++ b/test/ambiguous.jl
@@ -273,6 +273,8 @@ end
         pop!(need_to_handle_undef_sparam, first(methods(Core.Compiler.same_names)))
         pop!(need_to_handle_undef_sparam, which(Core.Compiler.convert, (Type{Union{Core.Compiler.Some{T}, Nothing}} where T, Core.Compiler.Some)))
         pop!(need_to_handle_undef_sparam, which(Core.Compiler.convert, (Type{Union{T, Nothing}} where T, Core.Compiler.Some)))
+        pop!(need_to_handle_undef_sparam, which(Core.Compiler.convert, Tuple{Type{Tuple{Vararg{Int}}}, Tuple{}}))
+        pop!(need_to_handle_undef_sparam, which(Core.Compiler.convert, Tuple{Type{Tuple{Vararg{Int}}}, Tuple{Int8}}))
         @test need_to_handle_undef_sparam == Set()
     end
     let need_to_handle_undef_sparam =
@@ -295,6 +297,8 @@ end
         pop!(need_to_handle_undef_sparam, which(Base.nonmissingtype, Tuple{Type{Union{Missing, T}} where T}))
         pop!(need_to_handle_undef_sparam, which(Base.convert, (Type{Union{Some{T}, Nothing}} where T, Some)))
         pop!(need_to_handle_undef_sparam, which(Base.convert, (Type{Union{T, Nothing}} where T, Some)))
+        pop!(need_to_handle_undef_sparam, which(Base.convert, Tuple{Type{Tuple{Vararg{Int}}}, Tuple{}}))
+        pop!(need_to_handle_undef_sparam, which(Base.convert, Tuple{Type{Tuple{Vararg{Int}}}, Tuple{Int8}}))
         @test need_to_handle_undef_sparam == Set()
     end
 end
diff --git a/test/tuple.jl b/test/tuple.jl
index 11dc498086226..3a22f3b089557 100644
--- a/test/tuple.jl
+++ b/test/tuple.jl
@@ -86,6 +86,9 @@ end
     end
 
     @test empty((1, 2.0, "c")) === ()
+
+    # issue #28915
+    @test convert(Union{Tuple{}, Tuple{Int}}, (1,)) === (1,)
 end
 
 @testset "size" begin