Efficient, realistic face animation is still a challenge. A system is proposed that yields realistic animations for speech. It starts from real 3D face dynamics, observed at a frame rate of 25 fps for thousands of points on the faces of speaking actors. When asked to animate a face it replicates the visemes that it has learned, and adds the necessary coarticulation effects. The speech animation could be based on as few as 16 modes, extracted through Independent Component Analysis from the observed face dynamics. Also faces for which only a static, neutral 3D model is available, can be animated. Rather than animating via verbatim copying other faces' deformation fields, the visemes are adapted to the shape of the new face. By localising this face in a 'Face Space', where also the locations of the example faces are known, visemes are adapted automatically according to the relative distance with respect to these examples. The animation tool proposes a good speech-based face animation as a point of departure for animators, who also get support by the system to then make further changes as desired.