As a tool for predicting stationary signals, the Least Mean Squares (LMS) algorithm is widely used. Its improvement, the family of normalised LMS algorithms, is known to outperform this algorithm. However, they still remain sensitive to selecting wrong parameters, being the learning coefficient μ and the signal history length M. We propose an improved version of both algorithms using a Fast Lane Approach, based on parallel evaluation of several competing predictors. These were applied to respiratory motion data from motion-compensated radiosurgery. Prediction was performed using arbitrarily selected values for the learning coefficient μ∈]0,0.3] and the signal history length M∈[1,15]. The results were compared to prediction using the globally optimal values of μ and M found using a grid search. When the learning algorithm is seeded using locally optimal values (found using a grid search on the first 96s of data), more than 44% of the test cases outperform the globally optimal result. In about 38% of the cases, the result comes to within 5% and, in about 9% of the cases, to within 5–10% of the global optimum. This indicates that the Fast Lane Approach is a robust method for selecting the parameters μ and M.