A memory device is provided comprising an array of memory cells. During a read operation, voltage on a read bit line will transition towards a second voltage level if a data value stored in that activated memory cell has a first value, and sense amplifier circuitry will then detect this situation. If that situation is not detected, the sense amplifier circuitry determines that the activated memory cell stores a second value. Bit line keeper circuitry is coupled to each read bit line and is responsive to an asserted keeper pulse signal to pull the voltage on each read bit line towards the first voltage level. Keeper pulse signal generation circuitry asserts the keeper pulse signal at a selected time. The selected time is such that the voltage on the associated read bit line will have transitioned to the trip voltage level before the keeper pulse signal is asserted.