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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.