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We explore how the reconstruction efficiency of fast spike population codes varies with population size, population composition and code complexity. Our study is based on experiments with moving light patterns which are projected onto the isolated retina of a turtle Pseudemys scripta elegans. The stimulus features to reconstruct are sequences of velocities kept constant throughout segments of 500 ms. The reconstruction is based on the spikes of a retinal ganglion cell (RGC) population recorded extracellularly via a multielectrode array. Subsequent spike sorting yields the parallel spike trains of 107 RGCs as input to the reconstruction method, here a discriminant analysis trained and tested in jack-knife fashion. Motivated by behavioral response times, we concentrate on fast reconstruction, i.e., within 150 ms following a trigger event defined via significant changes of the population spike rate. Therefore, valid codes involve only few (≤3) spikes per cell. Using only the latency t 1 of each cell (with reference to the trigger event) corresponds to the most parsimonious population code considered. We evaluate the gain in reconstruction efficiency when supplementing t 1 by spike times t 2 and t 3. Furthermore, we investigate whether sub-populations of smaller size benefit significantly from a selection process or whether random compilations are equally efficient. As selection criteria we try different concepts (directionality, reliability, and discriminability). Finally, we discuss the implications of a selection process and its inter-relation with code complexity for optimized reconstruction.