The masses of neutron-deficient nuclei close to A=80 are important formodeling 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 ⁵⁶Ni. 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, ^85,86,87,88Nb and ^96,98Mo have been measured in the precision trap of the JYFLTRAP Penning trap at IGISOL. The mass of ⁸⁴Zr 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.