Managing uncertainty in engineering design continues to challenge engineers. By combining the concept of regret from robust optimization with that of design space reduction from set-based design, a new complementary view on uncertainty referred to as Design Space Covering for Uncertainty (DSC-U) is introduced. This method develops a trade-space between reducing the design space and locking in sub-optimal performance while considering interval uncertainty that impacts the problem. A double-loop algorithm and a more efficient set covering algorithm are presented along with the structure of the method. These are demonstrated on three sample problems, a previously-studied cantilever tube optimization, the Rosenbrock function with different levels of coupling between the uncertain parameters, and a ship midship section design problem with thirty-six design variables and four uncertain terms. The DSC-U approach is shown to be practical in providing a complementary insight into the impact of uncertainty for a wide range of design techniques.