In current high density magnetic memory systems a large write current is used, giving its waveform a large overshoot. This often brings about severe excess saturation of the media so the recorded transition quality degrades. This problem has been overcome by constricting a portion of the write head yoke. This effectively places a flux control valve ahead of the write pole tip which reduces the sensitivity of the write field to the write current as well as to other parameters, thereby enabling the write field to rise very rapidly without an excessive increase in the write width and reducing its sensitivity to the write current at low current values.