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Weighted linear prediction (WLP) is a method to compute all-pole models of speech by applying temporal weighting of the residual energy. By using short-time energy (STE) as a weighting function, the algorithm over-weight those samples that fit the underlying speech production model well. The current work introduces a modified WLP method, stabilised weighted linear prediction (SWLP) leading always to stable all-pole models whose performance can be adjusted by changing the length (denoted by M) of the STE window. With a large M value, the SWLP spectra become similar to conventional LP spectra. A small value of M results in SWLP filters similar to those computed by the minimum variance distortionless response (MVDR) method. The study compares the performances of SWLP, MVDR, and conventional LP in spectral modelling of speech sounds corrupted by Gaussian additive white noise. Results indicate that SWLP is the most robust method against noise especially with a small M value.