Systems, methods, and devices of the various embodiments enable HTTP streaming that downloads different layers of the same media interval at different points of time before the play out time of that media interval. The various embodiments provide a download sequence that enables downloads of portions of a media interval to continue at different points in time until the play out position of the media presentation reaches a certain point with respect to the media interval. In an embodiment, the download sequence may rapidly adapt to changing network bandwidth conditions and may help ensure no stall occurs in media play out under minimum conditions. In an embodiment, the download sequence may provide an increased smoothing effect to reduce the rate of adaptation to changes in bandwidth, which may reduce the fluctuations in quality in the presence of repeated abrupt network changes.