Hase (bunny)

As you can imagine, "Hase" is also more commonly used for women than men. Real bunnies tend to be a bit cuter than mice, which may have to do with the fact that their classification as rodents was revoked back in 1912 (now they're so-called lagomorphs). Diminutives, by the way, can be used with just about any nickname - in this case it would be "Häschen."