This contribution is an extended in-depth study of our previously initial research work about the compact Log-periodic microstrip DGS lowpass filters. The improved filters proposed use a log-periodic zig-zag structure defected on the ground plane under a compensated microstrip line for microwave filter applications. More importantly, a comprehensive index called figure-of-merit (FoM) is introduced in this paper to characterize the achieved performance of this kind of filters. Results show that high FoMs can be realized for this contribution. The developed filters B and C have dimensions 30.307 mm × 31.17 mm and 22.35 mm × 31.524 mm, while the achieved FoMs for the two demonstrators are approximately 3.5×104 and 3.1×104, respectively.