Abstract In this paper, the performance of the recently proposed adaptive signal models on modeling speech voiceless stop sounds is presented. Stop sounds are transient parts of speech that are highly non-stationary in time. State-of-the-art sinusoidal models fail to model them accurately and efficiently, thus introducing an artifact known as the pre-echo effect. The adaptive QHM and the extended adaptive QHM (eaQHM) are tested to confront this effect and it is shown that highly accurate, pre-echo-free representations of stop sounds are possible using adaptive schemes. Results on a large database of voiceless stops show that, on average, eaQHM improves by 100% the Signal to Reconstruction Error Ratio (SRER) obtained by the standard sinusoidal model.