The paper continues in the exploration of the use of phrases as the basic unit for training and inference in neural text-to-speech (TTS) synthesis, namely using the VITS model. While most of the public TTS systems are trained on whole sentences or, in general, on longer chunks of speech, such systems may suffer from higher latency in applications where responsiveness is crucial. Although the use of shorter phrase-level inputs was shown to considerably reduce system latency, this was at the expense of some degradation in the quality of generated speech. In this paper, we explore several training strategies for using phrase-level data units. Finally, we were able to find a strategy that is capable of providing a synthesized speech quality competitive to the speech quality achieved when using whole sentences. All the evaluations are carried out on two different Czech voices.