Markov sources have been shown to be efficient pseudo-random pattern generators in SCAN-BIST. In this paper we give a new design for Markov sources. The new design first reduces the ATPG test set by removing the test cubes with low sampling probability and then produces test sequences based on a unique dynamic transition selection technique. Dynamic transition selection offers four transition options namely Markov source, inverted Markov source, fixed 0 and fixed 1. Experimental results show that the proposed design significantly reduces the test length to achieve 100% stuck-at fault coverage at the expense of a modest increase in the number of gates required to implement the test pattern generator.