Most radar systems determine the presence of a target via the comparison of the appropriate return (actually the output of a square-law device) to a threshold. In order to achieve CFAR (constant false-alarm rate) operation, this threshold must incorporate some estimate of the ambient noise power level, usually derived using measurements from a reference window of neighboring cells (in range, bearing, and/or doppler). Under the assumption that the reference celis are statistically homogeneous, cell-averaging (CA)-CFAR, which uses the empirical mean from the cells in the reference window as the noise power estimate, is optimal. However, the reference cells may contain interfering targets and/or clutter edges, and in such situations CA-CFAR performs poorly. Several alternative schemes have been proposed, but none appears to work well uniformly over the broad class of possible reference window nonhomogeneities. In this paper we investigate the use of the Li-filter, a MSE-optirni.zed amalgamation of ordered-statistic (L) and linear (1) ifiters, to form an estimate of the noise power. Our results show that Ll-CFAR, while in some situations suboptimal, appears to be robust to reference window nonuniformities.