  We introduce variants of the Ma-Dasgupta renormalization-group approach for
random quantum spin chains, in which the energy-scale is reduced by decimation
built on either perturbative or non-perturbative principles. In one
non-perturbative version of the method, we require the exact invariance of the
lowest gaps, while in a second class of perturbative Ma-Dasgupta techniques,
different decimation rules are utilized. For the S=1 random antiferromagnetic
Heisenberg chain, both type of methods provide the same type of disorder
dependent phase diagram, which is in agreement with density-matrix
renormalization-group calculations and previous studies.
