A system for programming non-volatile storage is proposed that reduces the impact of interference from the boosting of neighbors. Memory cells are divided into two or more groups. In one example, the memory cells are divided into odd and even memory cells; however, other groupings can also be used. Prior to a first trigger, a first group of memory cells are programmed together with a second group of memory cells using a programming signal that increases over time. Subsequent to the first trigger and prior to a second trigger, the first group of memory cells are programmed separately from the second group of memory cells using a programming signal that has been lowered in magnitude in response to the first trigger. Subsequent to the second trigger, the first group of memory cells are programmed together with the second group of memory cells with the programming signal being raised in response to the second trigger. Before and after both triggers, the first group of memory cells are verified together with the second group of memory cells.