For both reducing the ligament length and satellite droplet problems associated with producing high velocity ink droplets from an ink jet head printing at relatively high ink jet head-transport speeds, the ink jet head is driven by composite waveform including independent and successive first, second, and third electrical pulses (332,334,336), each having an exponential leading edge and a step-like trailing edge, the pulses having amplitudes, pulse widths (T 1 ,T 3 ,T 5 ), and dead times (T 2 ,T 4 ) between pulses, for causing the ink jet head to eject three successive ink droplets, each of increased velocity (V,, V 2 , V 3 ) relative to the preceding droplet, for causing the droplets to merge in flight to form a single or ultimate droplet (344) having a predetermined velocity (V4).