  In this paper, we developed new coding strategies for the Z-channel. In
particular, we look at the case with two-stage encoding. In this case, the
encoder uses noiseless feedback once and adjusts the further encoding strategy
based on the previous partial output of the channel. Nevertheless, the
developed codes improve the known results with full feedback for small length
and 1 error. A tool for the two-stage strategy is the development of a new
optimality condition for non-adaptive codes.
