A concrete example of one that sometimes gives me fits is F2L 15 (and the mirror, 16; this applies to both since I lump them together as "the same case" mentally but I'll use 15 as the example for the specifics).
My first instinct for the general case is to flip the corner's orientation by going over the top of the edge. To do the quickest flip and insert I can execute,
I end up with a rotation then a rotation back.
The above approach is more palatable to me when the edge is misoriented: split over the top, then rotate to orient for the insert. Edge was misoriented and I did exactly one 90 degree rotation, perfectly acceptable. But when I see the edge is already oriented I'd really, really like to be able to invoke a general "don't rotate" rule and this violates it. The first intuitive stab at addressing that problem is 100% equivalent:
flip the corner orientation with F layer turns rather than a rotation and L layer turns. Move efficient and rotationless but a little awkward and unflowing for me. Might just be a matter of practice.
An R turn is slot-safe with the slot's orientation so a different approach would be to flip the corner's orientation that way, bringing the bottom layer sticker to the top and resulting in a
rotationless, regripless, R/U 2-gen approach. Less move efficient but maybe trigger/finger-trick loaded enough to compensate.
After deconstructing, the one I think I'm sold on isn't as obvious. With the pair opposite the slot, a
sledgehammer will flip the corner's orientation without touching the edge, leaving a quick AUF and insert. Rotationless and I always welcome new members to the Department of Sledgehammer Abuse. Remains to be seen if this works as well while solving in anger as it does in theory. I do still think it's worth considering different ways of handling this case based on the edge orientation at the time, regardless.