Smoothed data maps permit the reader to identify general spatial trends by removing the background noise of random variability often present in raw data. To smooth mortality data from 798 small areas comprising the contiguous United States, we extended the head-banging algorithm to allow for differential weighting of the values to be smoothed. Actual and simulated data sets were used to determine how head-banging smoothed spike and edge features in the data, and to observe the degree to which weighting affected the results. As expected, spikes were generally removed while edges and clusters of high rates near the U.S. borders were maintained by the unweighted head-banging algorithm. Incorporating weights inversely proportional to standard errors had a substantial effect on smoothed data, for example determining whether observed spikes were retained or removed. The process used to obtain the smoothed data, including the choice of head-banging parameters, is discussed. Results are considered in the context of general spatial trends. Published in 1999 by John Wiley & Sons, Ltd. This article is a U.S. Government work and is in the public domain in the United States.