A method for programming a memory including a plurality of memory cells is provided. The method comprises selecting a current cell and executing a pre-program verify operation at a first program verify level. The method comprises executing a program and program verify operation for the current cell, including applying a sequence of program pulses and performing program verify steps. The sequence includes a starting pulse having a starting magnitude. The program verify steps use a second program verify level. The method also comprises determining the starting magnitude for a next cell as a function of a magnitude of the program pulse in an instance of the program verify step in which the current cell passes verify at the second program verify level.