  We consider the resummation of soft-gluon effects in heavy quark to heavy
quark decays, namely the processes Q1 -> Q2 + (non QCD partons), where Q1 and
Q2 are two different heavy quarks. We construct a new factorization scheme for
threshold resummed spectra, which allows us to consistently evaluate the
distribution of the final hadron invariant mass mX in all the kinematic
regions, i.e. when mX is smaller, of the same order, or larger than the mass of
the final quark Q2. A dependence of the Improved Coefficient Function on the
threshold variable is introduced, which can however be relegated to a small
interval of this variable by means of the so-called Partition of Unity. We
explicitly apply our improved scheme to the b -> X_s + gamma decay at
next-to-leading logarithmic accuracy.
