Existing methods for optimization of sequences by random mutagenesis generate libraries with a small number of mostly deleterious mutations, resulting in libraries containing a large fraction of non-functional clones that explore only a small part of sequence space. Large numbers of clones need to be screened to find the rare mutants with improvements. Library display formats are useful to screen very large libraries but impose screening limitations that limit the value of this approach for most commercial applications. By contrast, in both classical breeding and in DNA shuffling, natural diversity is permutated by homologous recombination, generating libraries of very high quality, from which improved clones can be identified with a small number of complex screens. Given that this small number of screens can be performed under the conditions of actual use of the product, commercially relevant improvements can be reliably obtained.