In this paper, the potential application of adaptive lattice equalisers based on gradient search adaptive algorithms, is examined. The assessment is based on simulations of equaliser performance in data communications systems which provides a comparison of the relative performance of these adaptive lattice equalisers with transversal equalisers. It highlights the critical balance between rapid convergence and degradation due to algorithm noise, which is involved when selecting the algorithm stepsize. Two new adaptive equaliser approaches are suggested, one based on a timed lattice structure feeding a linear combiner. The other is a short timed lattice structure in cascade with a transversal equaliser. Both approaches are shown to offer fast converging adaptive equalisers for data communications applications, which have a converged error performance superior to that of the direct application of a gradient adaptive lattice equaliser.