It does not have a perimeter strip but elastic bands on the 4 corners, which means it only fits rectangular mattresses. Unfortunately, it is useless for my oval (Stokke) one. It was advertised as "with strip" and that's why I bought it.

I got it for the exact size of my mattress and the elastic bands were fine. I don't know if they have made any changes or if it just happened to me. Anyway, it seems to do its job.

It does its job. I have no complaints. It is secured with elastic bands on the corners. I would prefer it to have a perimeter strap like the larger size. Maybe it is like that though to accommodate thin mattresses, like in a playpen.