During programming of storage elements, channel-to-floating gate coupling effects are compensated to avoid increased programming speed and threshold voltage distribution widening. In connection with a programming iteration, unselected bit lines voltages are stepped up to induce coupling to selected bit lines. Dedicated power supplies can be used to provide the step up to avoid a risk that the unselected bit lines begin floating due to pre-charging of other bit lines The selected bit lines are coupled higher as a function of their proximity to unselected bit lines, and in preparation for applying a program pulse. Coupling may be used for slow and fast programming modes. A dedicated power supply can be provided for driving slow programming mode bit lines at a level which provides coupling compensation.