Weekly series have characteristics which make seasonal adjustment inaccessible or unsatisfactory with most available software. These series are typically compiled for weeks ending on a given day of the week, Saturday in the application presented here. The number of Saturday’s within a year can be either 52 or 53 and their position varies from year to year. These features violate the basic periodic time series structure assumed by X-12-ARIMA (soon to be X-13ARIMA-SEATS), TRAMO/SEATS, and STAMP. A locally-weighted least squares procedure is suggested here, which can be used with a weekly design matrix having 52 or 53 observations in a year. The procedure starts from the regression method in Pierce, Grupe, and Cleveland (1984), which assumes a deterministic seasonal component. The method is currently being applied at the Bureau of Labor Statistics, the Federal Reserve, and the Bank of Canada.