In protein engineering, useful information may be gained from systematically generating and screening all single-point mutants of a given protein. We model and analyze an iterative two-stage procedure to generate all these mutants. At each position, L variants are generated in the first stage via saturation mutagenesis and are sequenced. In the second stage, the missing variants (out of the 19 possible single-point substitutions) are produced via site-directed mutagenesis. We study the economic tradeoff associated with varying L, and derive its optimal value given the experimental parameters.