Now before you get too upset about this seemingly bizarre superpower: this was 1958. Back then, it was not very unusual for ordinary people to have this ability (atomic testing, you know). So it makes sense that the writers of Superman #125 would endow the Man of Steel with it, too.
Jerry Coleman, Wayne Boring, and Stan Kaye titled their story "Superman's New Power!" In it, Superman faced several challenges that required that he be greatly reduced in size or be in multiple locations simultaneously. This necessitated the Mini-Me Superman. You can see several pages from this freaky issue at Comic Book Resources.
-via The Geek Twins