  We consider S=1/2 antiferromagnetic Heisenberg chains with alternating bonds
and quenched disorder, which represents a theoretical model of the compound
CuCl_{2x}Br_{2(1-x)}(\gamma-{pic})_2. Using a numerical implementation of the
strong disorder renormalization group method we study the low-energy properties
of the system as a function of the concentration, x, and the type of
correlations in the disorder. For perfect correlation of disorder the system is
in the random dimer (Griffiths) phase having a concentration dependent
dynamical exponent. For weak or vanishing disorder correlations the system is
in the random singlet phase, in which the dynamical exponent is formally
infinity. We discuss consequences of our results for the experimentally
measured low-temperature susceptibility of
CuCl_{2x}Br_{2(1-x)}(\gamma-{pic})_2.
