Studies of the acute health effects of air pollution have used exposure windows of different spans and related them to single-day responses. Little is known about whether an increased response window span might be a viable alternative to single-day responses. Our aim is to compare a new model specification where both the exposure and response variables are represented as 7 day moving averages (CMA&CMA model) with the most widely used model specifications in the literature, where the response variable is usually a single-day, in terms of coefficients and their precision and robustness. To this end, daily series of 12 emergency-related hospital admissions and 6 air pollutants spanning 5.5 years in Lisbon were analysed through single-pollutant linear regression and, when necessary M-estimation. With our data, the CMA&CMA model yields coefficients that are very close to models where only the exposure variable is specified as a moving average whether the latter are estimated by OLS or robust M-estimation. In addition, the CMA&CMA model leads to more precise and robust estimates than other model specifications. The new model specification is a straightforward tool for adjusting weekend effects and errors. It is also analogous to robust estimation, with the added advantages of being sensitive to extreme values that are clustered in time, and leading to more precise and robust estimates without loss of high-frequency information. One drawback is the induction of autocorrelation in the residuals. Copyright © 2009 John Wiley & Sons, Ltd.