The existing derivations of conventional fast RLS adaptive filters are intrinsically dependent on the shift structure in the input regression vectors. This structure arises when a tapped-delay line (FIR) filter is used as a modeling filter. In this paper, we show that a more general data structure is induced by other filter implementations, such as Laguerre-based filters and, more importantly, that an exact fast RLS algorithm can still be derived for such Laguerre-induced data structures.One of the benefits of working with a Laguerre basis is that fewer parameters can be used to model long impulse responses.