Speech generated by parametric synthesizers generally suffers from a typical buzziness, similar to what was encountered in old LPC-like vocoders. In order to alleviate this problem, a more suited modeling of the excitation should be adopted. For this, we hereby propose an adaptation of the Deterministic plus Stochastic Model (DSM) for the residual. In this model, the excitation is divided into two distinct spectral bands delimited by the maximum voiced frequency. The deterministic part concerns the low-frequency contents and consists of a decomposition of pitch-synchronous residual frames on an orthonormal basis obtained by Principal Component Analysis. The stochastic component is a high-pass filtered noise whose time structure is modulated by an energy-envelope, similarly to what is done in the Harmonic plus Noise Model (HNM). The proposed residual model is integrated within a HMM-based speech synthesizer and is compared to the traditional excitation through a subjective test. Results show a significative improvement for both male and female voices. In addition the proposed model requires few computational load and memory, which is essential for its integration in commercial applications.