Lambda Red recombineering is a powerful technique for making targeted genetic changes in bacteria. However, many applications are limited by the frequency of recombination. Previous studies have suggested that endogenous nucleases may hinder recombination by degrading the exogenous DNA used for recombineering. In this work, we identify ExoVII as a nuclease which degrades the ends of single-stranded DNA (ssDNA) oligonucleotides and double-stranded DNA (dsDNA) cassettes. Removing this nuclease improves both recombination frequency and the inheritance of mutations at the 3' ends of ssDNA and dsDNA. Extending this approach, we show that removing a set of five exonucleases (RecJ, ExoI, ExoVII, ExoX, and Lambda Exo) substantially improves the performance of co-selection multiplex automatable genome engineering (CoS-MAGE). In a given round of CoS-MAGE with ten ssDNA oligonucleotides, the five nuclease knockout strain has on average 46% more alleles converted per clone, 200% more clones with five or more allele conversions, and 35% fewer clones without any allele conversions. Finally, we use these nuclease knockout strains to investigate and clarify the effects of oligonucleotide phosphorothioation on recombination frequency. The results described in this work provide further mechanistic insight into recombineering, and substantially improve recombineering performance.