I find the sidepulls with the jowl strap stay put on my horses without the browband. The ones with the noseband and throatlatch need a browband. The Liz Graves one has nice rolled noseband, a jowl strap, throatlatch and browband, but I took the browband and throatlatch off. My mare has a big forelock and gets really sweaty under there with a browband. The Kaaren Jordan one is also very nice.
Cherie
