We address the problem of detecting slow-moving targets using a non-sideloking monostatic space-time adaptive processing (STAP) radar. The construction of optimum weights at each range implies the estimation of the clutter covariance matrix. This is typically done by straight averaging of neighboring data snapshots. The range-dependence of these snapshots generally results in poor performance. We present two new methods that handle the rangedependence by exploiting the geometry of the direction-Doppler curves.