We had a mini crib. Honestly, the jersey knit regular crib sheets fit it just fine (as long as you have the 5" mattress, not the 1" pad that comes with it). Pull it tight around the edges, we never had a problem. It was good and secure the entire 2 years my first kid was in it and the 1 year my second was.
I went NUTS trying to find sheets for the dang thing and the solution was so simple :-)