We have measured the radial velocity variation of the white dwarf secondary in the binary system containing the millisecond pulsar PSR J1012 + 5307. Combined with the orbital parameters of the radio pulsar, we infer a mass ratio q (=M-1/M-2) = 10.5 +/- 0.5 OUT optical spectroscopy has also allowed us to determine the mass of the white dwarf companion by fitting the spectrum to a grid of DA model atmospheres: we estimate M-2 = 0.16 +/- 0.02 M., and hence the mass of the neutron star is 1.64 +/- 0.22 M., where the error is dominated by that of M-2. The orbital inclination is 52 +/- 4 deg. For an initial neutron star mass of similar to 1.4 M., only a few tenths of a solar mass at most has been successfully accreted over the lifetime of the progenitor low-mass X-ray binary. If the initial mass of the secondary was similar to 1 M., our result suggests that the mass transfer may have been non-conservative.