The elastic task model (Buttazzo et al., 2002) is a powerful model for adapting real-time systems in the presence of uncertainty. This paper generalizes the existing elastic scheduling approach in several directions. It reveals that the original task compression algorithm in (Buttazzo et al., 2002) in fact solves a quadratic programming problem that seeks to minimize the sum of the squared deviation of a task's utilization from initial desired utilization. This finding indicates that the task compression algorithm may be applied to efficiently solve other similar types of problems. In particular, an iterative approach is proposed to solve the task compression problem for real-time tasks with deadlines less than respective periods. Furthermore, a new objective for minimizing the average difference of task periods from desired values is introduced and a closed-form formula is derived for solving the problem without recursion