Web servers are a popular target for adversaries as they are publicly accessible and often vulnerable to compromise. Compromises can go unnoticed for months, if not years, and recovery often involves a complete system rebuild. In this paper, we propose n-m-Variant Systems, an adversarial-resistant software rejuvenation framework for cloud-based web applications. We improve the state-of-the-art by introducing a variable m that provides a knob for administrators to tune an environment to balance resource usage, performance overhead, and security guarantees. Using m, security guarantees can be tuned for seconds, minutes, days, or complete resistance. We design and implement an n-m-Variant System prototype to protect a Mediawiki PHP application serving dynamic content from an external SQL persistent storage. Our performance evaluation shows a throughput reduction of 65% for 108 seconds of resistance and 83% for 12 days of resistance to sophisticated adversaries, given appropriate resource allocation. Furthermore, we use theoretical analysis and simulation to characterize the impact of system parameters on resilience to adversaries. Through these efforts, our work demonstrates how properties of cloud-based servers can enhance the integrity of Web servers.