A page of non-volatile multi-level storage elements on a word line WLn is sensed in parallel while compensating for perturbations from a neighboring page on an adjacent word line WLn+1. First, the programmed thresholds of storage elements on WLn+1 are sensed in the time domain and encoded as time markers. This is accomplished by a scanning sense voltage increasing with time. The time marker of a storage element indicates the time the storage element starts to conduct or equivalently when the scanning sense voltage has reached the threshold of the storage element. Secondly, the page on WLn is sensed while the same scanning voltage with an offset level is applied to WLn+1 as compensation. In particular, a storage element on WLn will be sensed at a time indicated by the time marker of an adjacent storage element on WLn+1, the time when the offset scanning voltage develops an appropriate compensating bias voltage on WLn+1.