The human voice is a directional sound source. This property has been explored for more than 200 years, mainly using measurements of human participants. Some efforts have been made to understand the anatomical parameters that influence speech directivity, e.g., the mouth opening, diffraction and reflections due to the head and torso, the lips and the vocal tract. However, these parameters have mostly been studied separately, without being integrated into a complete model or replica. The aim of this work was to study the combined influence of the torso, the lips and the vocal tract geometry on speech directivity. For this purpose, a simplified head and torso simulator was built; this simulator made it possible to vary these parameters independently. It consisted of two spheres representing the head and the torso into which vocal tract replicas with or without lips could be inserted. The directivity patterns were measured in an anechoic room with a turntable and a microphone that could be placed at different angular positions. Different effects such as torso diffraction and reflections, the correlation of the mouth dimensions with directionality, the higher-order modes and the increase in directionality due to the lips were confirmed and further documented. Interactions between the different parameters were found. It was observed that torso diffraction and reflections were enhanced by the presence of the lips, that they could be modified or masked by the effect of higher-order modes and that the lips tend to attenuate the effect of higher-order modes.