There's a family of encodings optimized for fitting the most information possible into an Unicode string of a given length, e.g. for gimmicks like fitting the most possible binary data into tweets.
For short messages in the mobile phone (i.e. GSM/3GPP) sense, which was my first association for "short message compression", it doubt that it works better than just sending binary messages with the appropriate header, but if that's not an option, it might just beat a custom alphabet based on the 7-bit GSM charset [1] (since that allows 100% of possible 7-bit characters to be used, whereas UTF-16 probably has at least some reserved codepoints that might be causing problems).
> 뮭䅰㼦覞㻪紹陠聚牊
I've never seen that before. The base64 below it, in contrast, is quite familiar.