Upon selecting non-volatile storage elements to be sensed, the system obtains information about the position of these non-volatile storage elements, determines sensing parameters based at least in part on this information, pre-charges a charge storage device and, while maintaining the voltage level of the bit lines of these memory cells at a constant value, applies a reference signal to these non-volatile storage elements for a certain duration of time, afterwards determining whether, for the certain duration of time, the current conducted by these non-volatile storage elements exceeds a predetermined value.