The accuracy of the conventional treatment of quark mass thresholds in the
QCD running coupling constant αs, based on the step approximation to
the β--function, is investigated. The errors of extrapolating \ase(\mu)
from low energies to μ=MZ, implied by this approximation, are shown to be
of the same magnitude as the typical next--to--next--to--leading order
contributions to \as and tend to increase the resulting \as. The importance of
the proper choice of matching points is emphasized.Comment: latex, 7 pages, 2 uuencoded figure
