There is growing evidence that much of the DNA in higher genomes is poly-functional, with the same nucleotide contributing to more than one type of code. Such poly-functional DNA should logically be multiply-constrained in terms of the probability of sequence improvement via random mutation. We describe a model of this relationship, which relates the degree of poly-functionality and the degree of constraint on mutational improvement. We show that: a) the probability of beneficial mutation is inversely related to the degree that a sequence is already optimized for a given code; b) the probability of beneficial mutation drastically diminishes as the number of overlapping codes increases. The growing evidence for a high degree of optimization in biological systems, and the growing evidence for multiple levels of poly-functionality within DNA, both suggest that mutations that are unambiguously beneficial must be especially rare. The theoretical scarcity of beneficial mutations is compounded by the fact that most of the beneficial mutations that do arise should confer extremely small increments of improvement in terms of total biological function. This makes such mutations invisible to natural selection. Beneficial mutations that are below a population's selection threshold are effectively neutral in terms of selection, and so should be entirely unproductive from an evolutionary perspective. We conclude that beneficial mutations that are unambiguous (not deleterious at any level), and useful (subject to natural selection), should be extremely rare.