Uniformization (also called Randomization, or Jensen’s method) is one of the most used techniques to compute the transient distribution of a Continuous Time Markov Chain. In this work we present a new variant of this method, which we call Mass Controlled Uniformization (MCU, for short). A central characteristic of MCU is that in many usually encountered situations it allows computing the transient distribution faster (sometimes orders of magnitude faster) than the commonly used Uniformization versions. This performance gain is mainly due to the selection of "the most relevant" state probabilities at each iteration of the algorithm, ignoring the very small ones, where the total accumulated error introduced by our selection approach is specified beforehand and can be as low as desired. MCU allows analyzing large Markovian models (say, with millions of states) in an efficient way. In some cases, however, MCU can perform slower than other current versions of Uniformization. In our work we identify these situations and propose a second approach, called Hybrid MCU (HMCU) that, in each iteration, adaptively behaves as MCU or as a selected standard Uniformization procedure. As a result, HMCU keeps the advantages of MCU, but in the worst case scenario behaves at the same level than the selected standard implementation of Jensen’s method.