Videoconferencing has become a ubiquitous medium for collaborative work. It does suffer however from various drawbacks such as zoom fatigue. This paper addresses the quality of user experience by exploring an enhanced system concept with the capability of conveying gaze and attention. Gazing Heads is a round-table virtual meeting concept that uses only a single screen per participant. It enables direct eye contact, and signals gaze via controlled head rotation. The technology to realise this novel concept is not quite mature though, so we built a camera-based simulation for four simultaneous videoconference users. We conducted a user study comparing Gazing Heads with a conventional “Tiled View” video conferencing system, for 20 groups of 4 people, on each of two tasks. The study found that head rotation clearly conveys gaze and strongly enhances the perception of attention. Measurements of turn-taking behaviour did not differ decisively between the two systems (though there were significant differences between the two tasks). A novel insight in comparison to prior studies is that there was a significant increase in mutual eye contact with Gazing Heads, and that users clearly felt more engaged, encouraged to participate and more socially present. Overall, participants expressed a clear preference for Gazing Heads. These results suggest that fully implementing the Gazing Heads concept, using modern computer vision technology as it matures, could significantly enhance the experience of videoconferencing.