  We analyze the constrained minimal supersymmetric standard model with mu>0
supplemented by a generalized `asymptotic' Yukawa coupling quasi-unification
condition, which allows an acceptable b-quark mass. We impose constraints from
the cold dark matter abundance in the universe, B physics, and the mass of the
lightest neutral CP-even Higgs boson. We find that, in contrast to previous
results obtained for a more restrictive Yukawa quasi-unification condition, the
lightest neutralino can act as a cold dark matter candidate in a relatively
wide parameter range. In this range, the lightest neutralino relic abundance is
drastically reduced mainly by stau-antistau coannihilations and, thus, the
upper bound on this abundance from cold dark matter considerations becomes
compatible with the recent data on the branching ratio of B_s --> mu^+mu^-.
Also, masses for the lightest neutral CP-even Higgs boson about (125-126) GeV,
favored by LHC, can be easily accommodated. The mass of the lightest
neutralino, though, comes out large (~1 TeV).
