Recent experiments have produced several Anopheles gambiae homing gene drives that disrupt female fertility genes, thereby eventually inducing population collapse. Such drives may be highly effective tools to combat malaria. One such homing drive, based on the zpg promoter driving CRISPR/Cas9, was able to eliminate a cage population of mosquitoes. A second version, purportedly improved upon the first by incorporating an X-shredder element (which biases inheritance towards male offspring), was similarly successful. Here, we re-analyze the data of each of these gene drives and suggest an alternative interpretation of their performance. We assess each suppression drive within an individual-based simulation framework that models mosquito population dynamics in continuous space. We find that the combined homing/X-shredder drive is actually less effective at population suppression within the context of our mosquito population model. In particular, the combined drive often fails to completely suppress the population, instead resulting in an unstable equilibrium between drive and wild-type alleles. By contrast, otherwise similar drives based on the nos promoter may prove to be more promising candidates for future development due to potentially superior performance.