A covariance-RLS lattice adaptive-filtering algorithm is presented. The algorithm permits nonzero initial conditions and need not 'warn' N-1 iterations in advance of the first iteration to preserve its low computational requirements. These are both improvements over previous lattice algorithms. The algorithm also has a slight computational advantage over previous solutions, rendering it more applicable to adaptive-filtering applications such as fast-starting adaptive equalizers and echo cancellers, where the initial data in the adaptive filter are not, and cannot be assumed to be, zero. >