  We perform an accurate computation of the production rate for primordial
black holes (PBHs). The reason is that the underlying mass variance had been
overestimated systematically, as was shown recently. For scale-free powerlaw
primordial spectra, and for a Universe with critical density, the mass variance
is less than 34% of its value thought earlier for the spectral index in the
range $1\leq n\leq 1.3$. We then extend our study to spectra with a
characteristic scale and find the accurate shape of the corresponding mass
variance. For a pure step in the primordial spectrum, the step in the variance
is smoothed around the characteristic scale $k_s$. For a spectrum with large
oscillations near $k_s$, we find a pronounced bump in the variance. This could
yield a significant part of the cold dark matter in the form of PBHs with mass
$M$ in the range $5\times 10^{15} {\rm g}\lesssim M \lesssim 10^{21} {\rm g}$.
