DEMs derived from dense remotely sensed measurements, including lidar- and radar-based DEMs, provide much greater surface detail than traditional interpolated DEMs but suffer from random noise that perturbs measures of surface shape such as slope and flow direction. Smoothing is an effective method of reducing noise but also tends to impact on important surface features, lowering hilltops, raising valleys and obliterating important fine detail. This paper describes a multiscale adaptives moothing approach that responds to both the relief and noise level in a DEM by smoothing aggressively where the noise is larger than the local relief and smoothing little or not at all where noise is less than relief. The method is simple and efficient and can be readily implemented in a raster GIS environment. The method is demonstrated on noisy SRTM data.