We extend Jensen?s time/utility functions and utility accrual model with the concept of joint utility functions (or JUFs) that allow an activity?s utility to be described as a function of the completion times of other activities and their progress. We also specify the concept of progressive utility that generalizes the previously studied imprecise computational model, by describing an activity?s utility as a function of its progress. Given such an extended utility accrual model, we consider the scheduling criterion of maximizing the weighted sum of completion time, progressive, and joint utilities. We present an algorithm called the Combined Utility Accrual algorithm (or CUA) for this criterion. Experimental measurements with an implementation of CUA on a POSIX RTOS illustrate the effectiveness of JUFs in a class of applications of interest to us.