Multipotent progenitors in the vertebrate retina often generate clonally related mixtures of excitatory and inhibitory neurons. The postmitotically expressed transcription factor, Ptf1a, is essential for all inhibitory fates in the zebrafish retina, including three types of horizontal and 28 types of amacrine cell. Here, we show that specific types of inhibitory neurons arise from the cell-autonomous influence of Ptf1a in the daughters of fate-restricted progenitors, such as Ath5 or Vsx1/2-expressing progenitors, and that in the absence of Ptf1a, cells that would have become these specific inhibitory subtypes revert to the histogenetically appropriate excitatory subtypes of the same lineage. Altered proportions of amacrine subtypes respecified by the misexpression of Ptf1a in the Ath5 lineage suggest that Ath5-expressing progenitors are biased, favoring the generation of some subtypes more than others. Yet the full array of inhibitory cell subtypes in Ath5 mutants implies the existence of Ath5-independent factors involved in inhibitory cell specification. We also show that an extrinsic negative feedback on the expression of Ptf1a provides a control mechanism by which the number of any and all types of inhibitory cells in the retina can be regulated in this lineage-dependent way.