Pattern detection in software systems is one of several collaborating techniques for reverse engineering and program comprehension. Unfortunately, it is a hard problem in both theory and practice. A recent method to increase efficiency is based on conservatively filtering edges of a software system's structure graph, i.e., only removing edges guaranteed not to be part of any pattern instance. This leads to planar graphs in many cases allowing for efficient matching algorithms. This paper shows the feasibility of a non-conservative filtering approach, where even edges possibly part of a pattern instance can be removed to reach planarity. We show theoretically that not only decreased accuracy is possible due to non-conservative filtering, but also increased accuracy. We also perform an experimental evaluation supporting this statement. The paper complements the safe filtering method and together the two approaches allow for efficient pattern detection for all systems and patterns.