I'll use a Piper Archer as an example:
From the POH
Vx is 64 KIAS. (flaps up)
Recommended short field takeoff procedure is to use flaps 25, rotate at 55 KIAS and climb at 60 KIAS until clearing obstacle. Then pitch down to accelerate. Flaps 10 passing 64 KIAS then flaps 0 and maintain 76 KIAS (Vy)
This procedure provided the shortest total distance from brake release to a 50' height above the runway during flight testing.