The nuclides 104-108Sn, 106-110Sb, 108,109Te, and 111I at the expected endpoint of the astrophysical rp process have been produced in 58Ni+natNi fusion-evaporation reactions at IGISOL and their mass values were precisely measured with the JYFLTRAP Penning trap mass spectrometer. For 106Sb, 108Sb, and 110Sb these are the first direct experimental mass results obtained. The related one-proton separation energies have been derived and the value for 106Sb, Sp=424(8) keV, shows that the branching into the closed SnSbTe cycle in the astrophysical rp process is weaker than expected.