The wubi input method (五笔字形) uses radical composition or something like it -- keys represent different (semi-arbitrary) character portions, and you "build" characters by choosing the portions, and adding other keys that indicate the overall shape of the character. You can get nearly any character out there in four keys, usually much less, and it also does phrase input. It's much harder to learn, obviously, but a practiced wubi typist is supposed to be able to go faster than pinyin.

Over the years I've tried to teach myself, and I can sort of do it, but I never got fast enough to really switch away from pinyin.