In sensing a page of nonvolatile memory cells with a corresponding group of sense modules in parallel, as each high current cell is identified, it is locked out from further sensing while others in the page continued to be sensed. The sense module involved in the locked out is then in a lockout mode and becomes inactive. A noise source from the sense module becomes significant when in the lockout mode. The noise is liable to interfere with the sensing of neighboring cells by coupling through its bit line to neighboring ones. The noise can also couple through the common source line of the page to affect the accuracy of ongoing sensing of the cells in the page. Improved sense modules and method isolate the noise from the lockout sense module from affecting the other sense modules still active in sensing memory cell in the page.