Why are default compose-key combinations not working?

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I enabled compose-key, and set it to be Caps Lock. It would work well, except the basic combinations aren't recognized (accented latin characters, for example, don't work).

Later, I installed xcompose, an alternative .XCompose file, placed in the home folder, and the combinations listed there work. For example, Compose, then "*", then "a" will type the letter Alpha, as expected. But Compose, then "apostrophe", then "e" won't type in the accented "e".

Where should I look?