Thank you very much, Tom, for asking the question, this is something I've puzzled over myself. In fact, I think I've even tried both and been corrected each time. Maybe I just guessed wrong in each particular case with amazing consistency. )-;
@manni3: So are you saying you can use either one any time, but the genitive is more traditionally correct and the accusative is more natural-sounding in normal conversation? Or what?
If so, I'm not sure that would explain why the genitive apparently sounds better to native speakers in certain collocations, and worse in others, independent of the diction level, that is, either in speech or in writing.
So far Irene's suggestion seems plausible. But if it doesn't ring a bell with any other German speakers, it may be just one of those wishful explanations we come up with because we wish language were that logical.
The other possibility, I would guess, is just that a few particular familiar collocations have coincidentally survived with the genitive, and everything else is accusative by default. But it would still help us as learners to know which collocations fall in that list.
So far there are more votes for 'eine Überlegung,' for instance, but one vote for 'einer Überlegung.' Any other examples or votes?