I ride my mare in a Jr. Cowhorse with the curb strap set really loose (it hardly does anything, I did this for less confusion between this bit and a snaffle as I switch between the two) and I recently rode her in a 3 piece snaffle mouth curb bit where the curbstrap was in effect. She worked good with it, so I tightened the curb strap on the Jr. Cowhorse.
I rode her with it today.
And had no brakes when I had to open her up to cut off a cow and calf. She normally has tons of brakes.