Velvet cap for eventing stadium round?

So I've started going to eventing schooling shows this year. Several times my show cap failed me and fell over my eyes during my stadium and XC rounds...not good. I'm having trouble finding a show cap that fits snug, while my Tipperary schooling helmets fits like a suction cup. Someone told me that for the stadium round, you have to wear the classic velvet show cap. Is that true, or can I get away with one of those more schooling type black skull caps?