Autohotkey is also useful for this. Any arbitrary set of characters can be auto replaced with the desired output, or alternatively be bound to a hotkey.
This removes the need to memorize some abstract set of Alt key sequences and instead one could type something such as ++degree to produce °. The sequence of characters could be anything to distinguish it from regularly used text, here using ++ and name of the symbol to illustrate.
I started writing my own WinCompose-like utility in AutoHotkey, before I learned about WinCompose. Gave up on that immediately, obviously.
AutoHotkey is really an amazing tool. The actual programming language is awkward, but it has capabilities no other tool offers without writing a bunch of tricky low-level C code yourself.
This removes the need to memorize some abstract set of Alt key sequences and instead one could type something such as ++degree to produce °. The sequence of characters could be anything to distinguish it from regularly used text, here using ++ and name of the symbol to illustrate.
WinCompose it appears uses a similar principle.