If you have nice grass and are just overseeding to keep it strong, I wouldn't go below about an inch and half.

If you need the new grass to basically replace a weak lawn, the lower you can go the better, imho. That sets the established grass back and give the new grass a better chance to establish.

But, the lower you go, the more work it is to do it best. Overseeding you don't want a bunch of debris left on top to interfere with seed/soil contact. That means cutting and bagging with several passes with a bagging mower. I have even needed a lawn vac sometimes. When you cut a yard that has alot of grass that low, it makes for large volumes of dead grass and thatch that need to be removed before overseeding.

I think 1.5 inches is about right. Are you slitseeding or core aerating before you seed? Also as some have mentioned, it may be worthwhile to delay fertilizing until after germination--your existing grass may bounce back faster than you'd like.