This paper presents the approach developed by the BUT team for the first DIHARD speech diarization challenge, which is based on our Bayesian Hidden Markov Model with eigenvoice priors system. Besides the description of the approach, we provide a brief analysis of different techniques and data processing methods tested on the development set. We also introduce a simple attempt for overlapped speech detection that we used for attaining cleaner speaker models and reassigning overlapped speech to multiple speakers. Finally, we present results obtained on the evaluation set and discuss findings we made during the development phase and with the help of the DIHARD leaderboard feedback.