The mass function for black holes and neutron stars at birth is explored for mass-losing helium stars. These should resemble, more closely than similar studies of single hydrogen-rich stars, the results of evolution in close binary systems. The effects of varying the mass-loss rate and metallicity are calculated using a simple semi-analytic approach to stellar evolution that is tuned to reproduce detailed numerical calculations. Though the total fraction of black holes made in stellar collapse events varies considerably with metallicity, mass-loss rate, and mass cutoff, from 5$%$ to 30$%$, the shapes of their birth functions are very similar for all reasonable variations in these quantities. Median neutron star masses are in the range 1.32 - 1.37 $M_odot$ regardless of metallicity. The median black hole mass for solar metallicity is typically 8 to 9 $M_odot$ if only initial helium cores below 40 $M_odot$ (ZAMS mass less than 80 $M_odot$) are counted, and 9 - 13 $M_odot$, in most cases, if helium cores with initial masses up to 150 $M_odot$ (ZAMS mass less than 300 $M_odot$) contribute. As long as the mass-loss rate as a function of mass exhibits no strong non-linearities, the black hole birth function from 15 to 35 $M_odot$ has a slope that depends mostly on the initial mass function for main sequence stars. These findings imply the possibility of constraining the initial mass function and the properties of mass loss in close binaries using ongoing measurements of gravitational wave radiation. The expected rotation rates of the black holes are briefly discussed.
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