Objective. The performance and usability of brain-computer interfaces (BCIs) can be improved by new paradigms, stimulation methods, decoding strategies, sensor technology etc. In this study we introduce new stimulation and decoding methods for electroencephalogram (EEG)-based BCIs that have targets flickering at the same frequency but with different phases. Approach. The phase information is estimated from the EEG data, and used for target command decoding. All visual stimulation is done on a conventional (60-Hz) LCD screen. Instead of the 'on/off' visual stimulation, commonly used in phase-coded BCI, we propose one based on a sampled sinusoidal intensity profile. In order to fully exploit the circular nature of the evoked phase response, we introduce a filter feature selection procedure based on circular statistics and propose a fuzzy logic classifier designed to cope with circular information from multiple channels jointly. Main results. We show that the proposed visual stimulation enables us not only to encode more commands under the same conditions, but also to obtain EEG responses with a more stable phase. We also demonstrate that the proposed decoding approach outperforms existing ones, especially for the short time windows used. Significance. The work presented here shows how to overcome some of the limitations of screen-based visual stimulation. The superiority of the proposed decoding approach demonstrates the importance of preserving the circularity of the data during the decoding stage.