Sadly, TinyCore [1] is hardly mentioned anymore when tiny distros are discussed, although still in development [2]. Maybe it's still just for a small niche of users, even after 15 years, but you can start with only 17MB's and add only the desired extensions [3].
[2] http://forum.tinycorelinux.net/index.php/topic,26201.0.html
[3] http://tinycorelinux.net/14.x/x86/tcz/
(not sure what their beef is with https...)
I do miss the times when their microcore was around 6-8MB's