If you can count on every printable ascii character being not-mangled, you can use ascii85/base85/Z85 (5 "ascii characters" to 4 bytes) instead of base64.
While a couple of people suggested Base65536, that encoding isn't particularly compact, and it can't be as elegant as 65536 would suggest because it has to dodge special cases in unicode.
It's almost always the case that either Base32768 is denser, or encodings with 2^17 or 2^20 characters are denser.