The application of “concentration” steps is the main principle behind Forgy’s k-means algorithm and Rousseeuw and van Driessen’s fast-MCD algorithm. Despite this coincidence, it is not completely straightforward to combine both algorithms for developing a clustering method which is not severely affected by few outlying observations and being able to cope with non spherical clusters. A sensible way of combining them relies on controlling the relative cluster scatters through constrained concentration steps. With this idea in mind, a new algorithm for the TCLUST robust clustering procedure is proposed which implements such constrained concentration steps in a computationally efficient fashion.