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.

WinCompose it appears uses a similar principle.