In this paper we examine a new penalty term for the Bayesian Information Criterion (BIC) that is suited to the problem of speaker diarization. Based on our previous approach of penalizing each cluster only with its effective sample size - an approach we called segmental - we propose a stricter penalty term. The criterion we derive retains the main property of the Segmental-BIC, i.e. it approximates the evidence of overall partitions of the data and simultaneously leads to a pairwise dissimilarity measure that is completely defined by the pair of clusters in question. The experimental results show significant improvement in diarization accuracy on the ESTER benchmark.