The fact that lattice and QR methods of adaptive least-squares filtering follow from the same geometric framework allows the first solution to the parameter identification problem using fast QR techniques. These relations suggest combining QR and lattice algorithms into hybrid algorithms of low complexity and good numerical behavior. It is emphasized that many other possibilities are available for mixing and matching the steps of QR and lattice algorithms. The various algorithms so obtained differ in their computational complexity, accessibility to desired variables, etc., but all work within a related geometric framework. >