A ramp-down programming voltage is used to program a group of nonvolatile memory cells in parallel, step by step from a highest step to a lowest step. Overall programming time is improved when a conventional setup for program inhibit together with a verify after each program step are avoided. A program voltage estimate is provided for each cell indicating the programming voltage expected to program the cell to its target. Initially, all but those cells having estimates at or above the current program voltage step will be program-inhibited. Thereafter, with each descending program voltage step, additional cells will be un-inhibited. Once un-inhibited, a cell need not be re-inhibited even if programmed to its target. This is because subsequent program steps are at lower voltages and ineffective in programming the cell beyond its target. The un-inhibit operation in one implementation amounts to simply pulling the associated bit lines to ground.