I'd prefer to know my new songs by heart too, but at my age it's not going to happen. How do I know? Songs I memorized a few years or months ago are completely gone.

I've decided that if I want to sing new songs at the Mudcat Singaround, I will have to have the words on paper. Of course, by the time I have typed it and practiced it, I have a good idea of how it goes and what rhymes with what.

By the way, nobody mentioned rhymes in the posts above. Rhymes help a lot with memorizing.
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When I wake up in the middle of the night, I often get myself back to sleep by "singing" a song I have recently memorized in my head. It shuts up the Inner Criticizer that attacks in the wee hours.