1. A method for execution by a computer to manage distributed computing of a task, the method comprises: ascertaining processing speeds of distributed storage and task (DST) execution units of a set of DST execution units performing like tasks on like data; receiving, by the set of DST execution units, a set of encoded data slices that includes a sub-set of data-based data slices and a sub-set of redundancy-based data slices; allocating performance of the task on the sub-set of data-based data slices to a sub-set of the set of DST execution units, wherein a first DST execution unit of the sub-set of DST execution units is allocated to perform a first partial task of the task on a first data-based data slice of the sub-set of data-based data slices on an encoded block by encoded block basis; and when, based on the ascertained processing speeds, a second DST execution unit of the set of DST execution units has a processing speed that is a threshold speed greater than a processing speed of the first DST execution unit: identifying at least one encoded block of the first data-based data slice for transferring processing responsibilities from the first DST execution unit to the second DST execution unit; obtaining the at least one encoded block by the second DST execution unit; and performing, by the second DST execution unit, a second partial task of the task on the at least one encoded block.