We examine the effect of inhibition on the axon initial segment (AIS) by the chandelier (“axoaxonic”) cells, using a simplified compartmental model of actual pyramidal neurons from cat visual cortex. We show that within generally accepted ranges, inhibition at the AIS cannot completely prevent action potential discharge: only small amounts of excitatory synaptic current can be inhibited. Moderate amounts of excitatory current always result in action potential discharge, despite AIS inhibition. Inhibition of the somadendrite by basket cells enhances the effect of AIS inhibition and vice versa. Thus the axoaxonic cells may act synergistically with basket cells: the AIS inhibition increases the threshold for action potential discharge, the basket cells then control the suprathreshold discharge.