Do Upsy Daisy wraps fit over all nappies?

Just wondering what people's experience with these is (the side snaps). The wings seem really narrow, looks like on any but the tightest setting part of the nappy might be left exposed at the top of the thigh? I know their nappies have a similar cut - are the wraps only designed to go over UD nappies or should they work with others too?

I have one of these and it's gorgeous ... but I find it's cut too high on the thigh to wear with most of the nappies I have