A method, and an associated system, for sending to a first group of recipients only the content portions of a continuity source data-flow which takes the form of ordered, successive, alternating content and non-content segments. From a methodologic point of view, the invention involves, in a manner which utilizes content-segment material buffering, delivering fully, and in correct order, to the first recipient group the material in each content segment, via steps including (a) bridging each gap between next-adjacent content segments at least partially with transmitted injection material that differs from the non-content segment material in the gap, which injection material ends in time no sooner than the end of the gap, and (b) employing, as needed, and as a part of such full delivering of content-segment material, time-progressive, time-length-variable buffering, and subsequent, progressive buffer-delivering, of any content-segment material which overlaps in time with the transmission of injection material.