A method for reading data from a data storage system, consisting of storing a plurality of copies of the data at a respective plurality of data storage units and receiving at a data port an access request submitted by a host to receive the data. The method further includes transmitting from the port, in response to the access request, a plurality of delivery requests for the data to the respective plurality of data storage units, transmitting from the plurality of data storage units to the port respective responses to the delivery requests, the responses including the data, and accepting at the port an earliest-arriving response consisting of the response to the delivery requests arriving first at the port. The data in the earliest-arriving response is forwarded from the port to the host.