This article investigates the effectiveness of potential partisan gerrymandering of the US House of Representatives across a range of states. We use a heuristic algorithm to generate district maps that optimize for multiple objectives, including compactness, partisan benefit, and competitiveness. While partisan gerrymandering is highly effective for both sides, we find that the majority of states are moderately biased toward Republicans when optimized for either compactness or partisan benefit, meaning that Republican gerrymanders have the potential to be more effective. However, we also find that more densely populated and more heavily Hispanic states show less Republican bias or even Democratic bias. Additionally, we find that in almost all cases we can generate reasonably compact maps with very little sacrifice to partisan objectives through a mixed‐objective function. This suggests that there is a strong potential for stealth partisan gerrymanders that are both compact and beneficial to one party. Nationwide, partisan gerrymandering is capable of swinging over 100 seats in the US House, even when compact districts are simultaneously sought.