The Rad51/RecA family of recombinases perform a critical function in typical repair of double-strand breaks (DSBs): strand invasion of a resected DSB end into a homologous double-stranded DNA (dsDNA) template sequence to initiate repair. However, repair of a DSB using single stranded DNA (ssDNA) as a template, a common method of CRISPR/Cas9-mediated gene editing, is Rad51-independent. We have analyzed the genetic requirements for these Rad51-independent events in Saccharomyces cerevisiae by creating a DSB with the site-specific HO endonuclease and repairing the DSB with 80-nt single-stranded oligonucleotides (ssODNs), and confirmed these results by Cas9-mediated DSBs in combination with a bacterial retron system that produces ssDNA templates in vivo. We show that single strand template repair (SSTR), is dependent on Rad52, Rad59, Srs2 and the Mre11-Rad50-Xrs2 (MRX) complex, but unlike other Rad51-independent recombination events, independent of Rdh54. We show that Rad59 acts to alleviate the inhibition of Rad51 on Rad52's strand annealing activity both in SSTR and in single strand annealing (SSA). Gene editing is Rad51-dependent when double-stranded oligonucleotides of the same size and sequence are introduced as templates. The assimilation of mismatches during gene editing is dependent on the activity of Msh2, which acts very differently on the 3' side of the ssODN which can anneal directly to the resected DSB end compared to the 5' end. In addition DNA polymerase Polδ's 3' to 5' proofreading activity frequently excises a mismatch very close to the 3' end of the template. We further report that SSTR is accompanied by as much as a 600-fold increase in mutations in regions adjacent to the sequences directly undergoing repair. These DNA polymerase ζ-dependent mutations may compromise the accuracy of gene editing.