The masses of neutron-deficient nuclei close to A=80 are important for modeling the astrophysical rapid proton capture process (rp process) [1]. The rp process occurs as a sequence of β + -decays and proton captures in various astrophysical sites, such as on the surface of an accreting neutron star. The rp process flows close to the N = Z nuclei up to 56 Ni. At higher masses, the path will broaden and shift by about one or two units towards stable nuclei. The decay properties of several neutron-deficient nuclei near A=80 have been studied at the IGISOL facility in a series of experiments [2]. These investigations are now extended to precision mass measurements of the nuclei. The masses of 79,80,81,82,83 Y, 83,84,85,86,88 Zr, 85,86,87,88 Nb and 96,98 Mo have been measured in the precision trap of the JYFLTRAP Penning trap at IGISOL. The mass of 84 Zr has been measured for the first time. The accuracy of the Q EC values and proton separation energies, which are important for the rp process, could be improved significantly for the studied neutron-deficient nuclei.