Meiotic DNA double-strand breaks (DSBs) initiate crossover (CO) recombination, which is necessary for accurate chromosome segregation, but DSBs may also repair as non-crossovers (NCOs). Multiple recombination pathways with specific intermediates are expected to lead to COs and NCOs. We revisited the mechanisms of meiotic DSB repair and the regulation of CO formation, by conducting a genome-wide analysis of strand-transfer intermediates associated with recombination events. We performed this analysis in a SK1 × S288C Saccharomyces cerevisiae hybrid lacking the mismatch repair (MMR) protein Msh2, to allow efficient detection of heteroduplex DNAs (hDNAs). First, we observed that the anti-recombinogenic activity of MMR is responsible for a 20% drop in CO number, suggesting that in MMR-proficient cells some DSBs are repaired using the sister chromatid as a template when polymorphisms are present. Second, we observed that a large fraction of NCOs were associated with trans-hDNA tracts constrained to a single chromatid. This unexpected finding is compatible with dissolution of double Holliday junctions (dHJs) during repair, and it suggests the existence of a novel control point for CO formation at the level of the dHJ intermediate, in addition to the previously described control point before the dHJ formation step. Finally, we observed that COs are associated with complex hDNA patterns, confirming that the canonical double-strand break repair model is not sufficient to explain the formation of most COs. We propose that multiple factors contribute to the complexity of recombination intermediates. These factors include repair of nicks and double-stranded gaps, template switches between non-sister and sister chromatids, and HJ branch migration. Finally, the good correlation between the strand transfer properties observed in the absence of and in the presence of Msh2 suggests that the intermediates detected in the absence of Msh2 reflect normal intermediates.