Testing of digital circuits seems to be a completely mastered part of the design flow, but constrained test patterns generation is still a highly evolving branch of digital circuit testing. Our previous research on constrained test pattern generation proved that we can benefit from an implicit representation of test patterns set in CNF (Conjunctive Normal Form). Some techniques of speeding up the constrained SAT-based test patterns generation are described and closely analyzed in this paper. These techniques are experimentally evaluated on a real SAT-based algorithm performing a constrained test patterns compression based on overlapping of test patterns. Experiments are performed on a subset of ISCAS'85 and '89 benchmark circuits. Results of the experiments are discussed and recommendations for a further development of similar SAT-based tools for constrained test patterns generation are given.