  We present a new empirical prescription for the mass-loss rates of carbon and
oxygen sequence Wolf-Rayet stars as a function of their luminosity, surface
chemical composition, and initial metallicity. The new prescription is based on
results of detailed spectral analyses of WC and WO stars, and improves the
often applied Nugis & Lamers (2000) relation. We find that the mass-loss rates
of WC and WO stars (with $X=0$ and $Y < 0.98$) can be expressed as
$\log{\dot{M}} = -9.20 + 0.85\log{(L/L_{\odot})} + 0.44\log{Y} +
0.25\log{(Z_{\mathrm{Fe}}/Z_{\mathrm{Fe}, \odot})}$. This relation is based on
mass-loss determinations that assume a volume-filling factor of 0.1, but the
prescription can easily be scaled to account for other volume-filling factors.
The residual of the fit is $\sigma = 0.06$ dex. We investigated whether the
relation can also describe the mass loss of hydrogen-free WN stars and showed
that it can when an adjustement of the metallicty dependence ($\log{\dot{M}}
\propto 1.3\log{(Z_{\mathrm{Fe}}/Z_{\mathrm{Fe}, \odot})}$) is applied.
Compared to Nugis & Lamers (2000), $\dot{M}$ is less sensitive to the
luminosity and the surface abundance, implying a stronger mass loss of massive
stars in their late stages of evolution. The modest metallicity dependence
implies that if WC or WO stars are formed in metal deficient environments,
their mass-loss rates are higher than currently anticipated. These effects may
result in a larger number of type Ic supernovae and less black holes to be
formed, and may favour the production of superluminous type Ic supernovae
through interaction with C and O rich circumstellar material or the dense
stellar wind.
