Hi Maria:
I think there are few instances that student's "deserve" extra credit. For me, that's like saying, "I'll give extra points to some students but not others".
Now I know you don't mean it that way, but if extra credit is important, I think it should just be a part of the regular curriculum and available (and expected) of all students.
Things like dropping the lowest quiz or a bonus point on a final example - those make sense because they relate to learning. Having students choose not to do some things then wanting credit for other things just… >>>