  We determine the improvement coefficients b_m and b_a-bp in quenched lattice
QCD for a range of beta-values, which is relevant for current large scale
simulations. At fixed beta, the results are rather sensitive to the precise
choices of parameters. We therefore impose improvement conditions at constant
renormalized parameters, and the coefficients are then obtained as smooth
functions of g_0^2. Other improvement conditions yield a different functional
dependence, but the difference between the coefficients vanishes with a rate
proportional to the lattice spacing. We verify this theoretical expectation in
a few examples and are therefore confident that O(a) improvement is achieved
for physical quantities. As a byproduct of our analysis we also obtain the
finite renormalization constant which relates the subtracted bare quark mass to
the bare PCAC mass.
