The UN Sustainable Development Goal, SDG 7.3, is to double the global rate of improvement in energy efficiency by 2030. To meet this and other energy targets, countries encourage the development and adoption of energy-efficient products. An extensively researched phenomenon in this context is the energy rebound effect, especially in transportation. However, the direct relationship between the energy rebound effect and car emission levels has barely been investigated. Understanding this relationship is important, because energy-related emissions are closely linked to mortality, morbidity, and climate change. We assess the emission consequences in the private car market in Israel of a rebound effect associated with a policy promoting energy-efficient cars. We find that the baseline rebound before introduction of the policy was 40%. In the following three periods marked by policy changes, it grew to 54%, 69%, and 88%. Using household data with specific car characteristics and usage, we calculate the added greenhouse gas (GHG) emission consequences of this rebound by the end of the studied period to be about 5% of the country's per-capita target. Notably, estimates for the emission consequences using "average car" values were almost twice as high. The reason for this gap derives from the co-dependance between car usage and car efficiency. We discuss the implications of this gap in meeting emission goals.