Normalized excess mixing ratios (NEMRs), also known as enhancement ratios, are a common way to characterize plumes of pollution in atmospheric research. As single-source pollutant plumes disperse in the atmosphere, they are diluted by mixing with the adjacent background air. Changes in the composition of this background air can cause large changes to the NEMR that is subsequently measured by remote-sensing, airborne, or ground-based instruments. This scenario is common when boundary layer plumes enter the free troposphere and could also impact long-range transport or plumes near the top of the troposphere. We provide a context for these issues and an example showing that neglect of this effect could lead to serious errors in data interpretation.