The DNA structure-selective endonuclease Mus81-Mms4/Eme1 incises a number of nicked joint molecule substrates in vitro. 3'-flaps are an excellent in vitro substrate for Mus81-Mms4/Eme1. Mutants in MUS81 are synthetically lethal with mutations in the 5'-flap endonuclease FEN1/Rad27 in Saccharomyces cerevisiae and Schizosaccharomyces pombe. Considering the possibility for isoenergetic interconversion between 3'- and 5'- flaps, these data are consistent with the hypothesis that Mus81-Mms4/Eme1 acts on 3'-flaps in vivo. FEN1/Rad27 prefers dually flapped substrates and cleaves in a way that allows direct ligation of the resulting nick in the product duplex. Here we test the activity of Mus81-Mms4 on dually flapped substrates and find that in contrast to FEN1/Rad27, Mus81-Mms4 activity is impaired on such substrates, resulting in cleavage products that do not allow direct religation. We conclude that Mus81-Mms4, unlike FEN1/Rad27, does not prefer dually flapped substrates and is unlikely to function as a 3'-flapase counterpart to the 5'-flapase activity of FEN1/Rad27. We further find that joint molecule incision by Mus81-Mms4 occurs in a fashion determined by the branch point, regardless of the position of an upstream duplex end. These findings underscore the significance of a nick adjacent to a branch point for Mus81-Mms4 incision.