Despite exciting prospects, the development of 360 • videos is persistently hindered by the difficulty to stream them. To reduce the data rate, existing streaming strategies adapt the video rate to the user's Field of View (FoV), but the difficulty of predicting the FoV and persistent lack of bandwidth are important obstacles to achieve best experience. In this article we exploit the recent findings on human attention in VR to introduce a new additional degree of freedom for the streaming algorithm to leverage: Virtuall Walls (VWs) are designed to translate bandwidth limitation into a new type of impairment allowing to preserve the visual quality by subtly limiting the user's freedom in well-chosen periods. We carry out experiments with 18 users and confirm that, if the VW is positioned after the exploration phase in scenes with concentrated saliency, a substantial fraction of users seldom perceive it. With a double-stimulus approach, we show that, compared with a reference with no VW consuming the same amount of data, VW can improve the quality of experience. Simulation of different FoV-based streaming adaptations with and without VW show that VW enables reduction in stalls and increases quality in FoV.