1. A method comprises: receiving data segments of a data stream to produce received data segments; in order of receiving the data segments: encrypting a data segment of the received data segments to produce an encrypted data segment; dispersed storage error encoding the encrypted data segment to produce a set of encoded data slices; buffering at least a number of encoded data slices of the set of encoded data slices in accordance with a threshold setting to produce first buffered encoded data slices; and when the threshold setting is less than a pillar width value, buffering remaining encoded data slices of the set of encoded data slices in accordance with the threshold setting to produce second buffered encoded data slices; and when a number of first buffered encoded data slices compares favorably to an outputting threshold, outputting the first buffered encoded data slices and, at most, some of the second buffered encoded data slices in accordance with a pseudo random output sequencing order.