The Affordable Clean Energy (ACE) rule, the US Environmental Protection Agency's (EPA) proposed replacement of the Clean Power Plan (CPP), targets heat rate improvements (HRIs) at individual coal plants in the US. Due to greater plant efficiency, such HRIs could lead to increased generation and emissions, known as an emissions rebound effect. The EPA Regulatory Impact Analysis for the ACE and other analyses to date have not quantified the magnitude and extent of an emissions rebound. We analyze the estimated emissions rebound of carbon dioxide (CO2) and criteria pollutants sulfur dioxide (SO2) and nitrogen oxides (NOX ), using results from the EPA's power sector model, under the ACE in 2030 at model coal plants and at the state and national levels compared to both no policy and the CPP. We decompose emissions changes under a central illustrative ACE scenario and find evidence of a state-level rebound effect. Although the ACE reduces the emissions intensity of coal plants, it is expected to increase the number of operating coal plants and amount of coal-fired electricity generation, with 28% of model plants showing higher CO2 emissions in 2030 compared to no policy. As a result, the ACE only modestly reduces national power sector CO2 emissions and increases CO2 emissions by up to 8.7% in 18 states plus the District of Columbia in 2030 compared to no policy. We also find that the ACE increases SO2 and NOX emissions in 19 states and 20 states plus DC, respectively, in 2030 compared to no policy, with implications for air quality and public health. We compare our findings to other model years, additional EPA ACE scenarios, and other modeling results for similar policies, finding similar outcomes. Our results demonstrate the importance of considering the emissions rebound effect and its effect on sub-national emissions outcomes in evaluating the ACE and similar policies targeting HRIs.