High fuel economy is typically achieved with smooth velocity profiles, which can be attained with slow engine response. The reverse however, is not true. Specifically, this paper shows that slow engine response may have deleterious fuel economy effects when aggressive profiles such as the US06 drive cycle need to be tracked. This effect is crucial for strategies which enable higher fuel efficiency at the expense of engine responsiveness. It is shown that slow engine dynamics lead to fluctuations in vehicle tracking performance that result in higher fuel consumption. The effect is quantified with a mean value model of a vehicle with a turbocharged engine undergoing the US06 drive cycle with two different strategies, trading off fuel economy and turbo-lag. The strategies include one that minimizes the engine backpressure through wastegate control (MBWG) and another that uses low pressure loop cooled exhaust gas recirculation (LP-cEGR) in addition to the MBWG strategy. The results indicate that slower engine dynamics can completely overshadow (in the LP-cEGR case) or even reverse (in the MBWG case) these strategies' fuel economy gains.