Recently the observationally derived stellar-wind mass-loss rates for Wolf-Rayet stars, or massive naked helium stars, have been revised downwards by a substantial amount. We present evolutionary calculations of helium stars incorporating such revised mass-loss rates, as well as mass transfer to a close compact binary companion. Our models reach final masses well in excess of 10 M⊙, consistent with the observed masses of black holes in X-ray binaries. This resolves the discrepancy found with previously assumed high mass-loss rates between the final masses of stars which spend most of their helium-burning lifetime as Wolf-Rayet stars (˜3 M⊙) and the minimum observed black hole masses (6 M⊙). Our calculations also suggest that there are two distinct classes of progenitors for Type Ic supernovae: one with very large initial masses (35 M⊙), which are still massive when they explode and leave black hole remnants, and one with moderate initial masses (˜12–20 M⊙) undergoing binary interaction, which end up with small pre-explosion masses and leave neutron star remnants.