The "impartial trimming" methodology in clustering analysis was initially designed (see Cuesta-Albertos et al., 1997) to gain protection against outliers and bridging objects (objects intermediate between clusters). In this work the methodology is applied to best k-nets. We include a study of optimal regions, which parallels that of trimmed k-means, showing that only non-pathological regions arise from impartial trimming procedures. Also we prove the strong consistency of the method by suitably varying the level of trimming with the size of the sample. A section is devoted to comparing the performance in a real data set of the suggested procedure with that of trimmed k-means.