Control over voice quality, e.g. breathy and tense voice, is important for speech synthesis applications. For example, transformations can be used to modify aspects of the voice re- lated to speaker's identity and to improve expressiveness. How- ever, it is hard to modify voice characteristics of the synthetic speech, without degrading speech quality. State-of-the-art sta- tistical speech synthesisers, in particular, do not typically al- low control over parameters of the glottal source, which are strongly correlated with voice quality. Consequently, the con- trol of voice characteristics in these systems is limited. In con- trast, the HMM-based speech synthesiser proposed in this paper uses an acoustic glottal source model. The system passes the glottal signal through a whitening filter to obtain the excitation of voiced sounds. This technique, called glottal post-filtering, allows to transform voice characteristics of the synthetic speech by modifying the source model parameters. We evaluated the proposed synthesiser in a perceptual ex- periment, in terms of speech naturalness, intelligibility, and similarity to the original speaker's voice. The results show that it performed as well as a HMM-based synthesiser, which generates the speech signal with a commonly used high-quality speech vocoder.