Methane-a short-lived and potent greenhouse gas-presents a unique challenge: it is emitted from a large number of highly distributed and diffuse sources. In this regard, the United States' Environmental Protection Agency (EPA) has recommended periodic leak detection and repair surveys at oil and gas facilities using optical gas imaging technology. This regulation requires an operator to fix all detected leaks within a set time period. Whether such 'find-all-fix-all' policies are effective depends on significant uncertainties in the character of emissions. In this work, we systematically analyze the effect of facility-related and mitigation-related uncertainties on regulation effectiveness. Drawing from multiple publicly-available datasets, we find that: (1) highly-skewed leak-size distributions strongly influence emissions reduction potential; (2) variations in emissions estimates across facilities leads to large variability in mitigation effectiveness; (3) emissions reductions from optical gas imaging-based leak detection programs can range from 15% to over 70%; and (4) while implementation costs are uniformly lower than EPA estimates, benefits from saved gas are highly variable. Combining empirical evidence with model results, we propose four policy options for effective methane mitigation: performanceoriented targets for accelerated emission reductions, flexible policy mechanisms to account for regional variation, technology-agnostic regulations to encourage adoption of the most costeffective measures, and coordination with other greenhouse gas mitigation policies to reduce unintended spillover effects.