A float-responsive valve includes a valve actuator that is selectively responsive to operation of a float to move from a first position to a second position in which the valve actuator holds the valve element in its open position. When the valve actuator is in the second position thereof, fluid pressure that would otherwise tend to force the valve element toward its seat is essentially incapable of closing the valve element. Preferably, a force vector applied through a flapper-type valve actuator forms an essentially nonnegative, more preferably generally collinear, angle with a bisector line passing through a pivot axis of the valve actuator and a primary contact point between the valve actuator and the flapper.