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This paper presents the adaptation of HMM-based speech synthesis to laughter signals. Acoustic laughter synthesis HMMs are built with only 3 minutes of laughter data. An evaluation experiment shows that the method achieves significantly better performance than previous works. In addition, the first method to generate laughter phonetic transcriptions from high-level signals (in our case, arousal signals) is described. This enables to generate new laughter phonetic sequences, that do not exist in the original data. The generated phonetic sequences are used as input for HMM synthesis and reach similar perceived naturalness as laughs synthesized from existing phonetic transcriptions. These methods open promising perspectives for the integration of natural laughs in man-machine interfaces. It could also be used for other vocalizations (sighs, cries, coughs, etc.).