During meiosis programmed DNA double-strand breaks (DSBs) are repaired by homologous recombination using the sister chromatid or the homologous chromosome (homolog) as a template. This repair results in crossover (CO) and non-crossover (NCO) recombinants. Only CO formation between homologs provides the physical linkages guiding correct chromosome segregation, which are essential to produce healthy gametes. The factors that determine the CO/NCO decision are still poorly understood. Using Schizosaccharomyces pombe as a model we show that the Rad51/Dmc1-paralog complexes Rad55-Rad57 and Rdl1-Rlp1-Sws1 together with Swi5-Sfr1 play a major role in antagonizing both the FANCM-family DNA helicase/translocase Fml1 and the RecQ-type DNA helicase Rqh1 to limit hybrid DNA formation and promote Mus81-Eme1-dependent COs. A common attribute of these protein complexes is an ability to stabilize the Rad51/Dmc1 nucleoprotein filament, and we propose that it is this property that imposes constraints on which enzymes gain access to the recombination intermediate, thereby controlling the manner in which it is processed and resolved. 