Dangerous Stairs

Hi. We're going to be moving into our new house in a week and a half and I'm very worried about the stairs leading up to where two of our children will be. The house was originally one story. Some years ago the attic was finished and these stairs were installed. The stair treads are carpeted, of average height, but they're shallow. Going up them is no problem, but our don't fit on them properly going down. In order to get a decent footing with our toes, we have to turn sideways a little to fit our whole foot on the tread. I'm just so worried that one of our girls is going to come hurrying, just once, down those stairs and have an accident. We're considering a spiral staircase, but I'm not sure that will work because I believe the cellar stairs run below these stairs. We're also considering getting rid of one step and making each of the stairs higher, giving room to make them deeper, but that seems just as dangerous. Is there a very logical solution to this problem? Any suggestions? Thanks! Lynne