I don't know so many flights which are really shorter than 250 nm and which for you can buy tickets, i.e. which is served by an airline...
There is a definition in Europe which says, a short haul flight is everything that is 810 nm (1500 km) or shorter. In this category, we know a lot of examples:
EDDL - LIRF
EDDL - LOWW
EDDL - LIMC
... . . . . .....
So, the case that you've described is the short haul amongst the short haul flights. And even in this category which I call "super short haul", there is a difference (concerning the alt that you should not exceed) between
EDDL - EBLG
[which is an example for "is not served by an airline"]
EDDL - EDDH
[which in fact IS served by an airline...
So, can you give an example? Which flight are you looking for?