Fast segment reconstruction from erasure-coded fragments, including the steps of requesting, by an assembling device using a fragment pull protocol, from a plurality of fractional-storage servers, a first quantity of erasure-coded fragments associated with one or more segments of streaming content; the first quantity of fragments is requested approximately according to the sequential order of the segments, and the first quantity of fragments is more than the minimal quantity of fragments needed for reconstructing the one or more segments. And receiving, by the assembling device, a second decodable quantity of fragments as a response; whereby the second quantity of fragments may be smaller than the first quantity due to a failure condition.