Power-saving techniques are employed in sensing a group of non-volatile memory cells in parallel. One technique is that the coupling of the memory cells to their bit lines is delayed during a precharge operation in order to reduce the cells' currents working against the precharge. Another technique is that a power-consuming precharge period is minimized by preemptively starting the sensing in a multi-pass sensing operation. High current cells not detected as a result of the premature sensing will still be able to be detected in a subsequent pass.