When evaluating quantitative measures of complex systems using Markov models, a major drawback is the size of the generated state space, due to the intrinsic combinatorics associated with these models. If the number of states is excessively large, the model may be simply untractable. Observe also that in some cases, infinite models are appropriate, in which case, except for particular structures, the numerical procedures are not applicable. Recently, methods have been proposed to deal with this problem. The idea is to derive bounds of the measures of interest, by replacing a large part of the state space by some compact information. This has been done mainly for asymptotic dependability measures, and the proposed methods are valid under specific and restrictive conditions. In this paper, we extend these techniques to more general cases. In particular, we show that our approach can also give tight bounds of performance measures. We also show how to handle, in some cases, infinite models. We illustrate the new method with some analytically untractable open queueing networks, as well as with dependability models that cannot be analyzed by previous proposed techniques.