I prefer
Millie on its own,
Mildred is still too old-lady-ish to me. Some more appealing "Mil-" names are:
Milda Milena Milla Millaray Milana
and
Camilla nn
Milly /
Millie
"Night fell, lots of large stars came out, and the Hemulen loved his park all the better. It was wide and mysterious; one could lose one's way in it and still be at home."
-Tove Jansson