In testing, engineers want to run the most useful tests early (prioritization). When tests are run hundreds or thousands of times, minimizing a test set can result in significant savings (minimization). This paper proposes a new analysis technique to address both the minimal test set and the test case prioritization problems. This paper precisely defines the concept of mutant stubbornness, which is the basis for our analysis technique. We empirically compare our technique with other test case minimization and prioritization techniques in terms of the size of the minimized test sets and how quickly mutants are killed. We used seven C language subjects from the Siemens Repository, specifically the test sets and the killing matrices from a previous study. We used 30 different orders for each set and ran every technique 100 times over each set. Results show that our analysis technique performed significantly better than prior techniques for creating minimal test sets and was able to establish new bounds for all cases. Also, our analysis technique killed mutants as fast or faster than prior techniques. These results indicate that our mutant stubbornness technique constructs test sets that are both minimal in size, and prioritized effectively, as well or better than other techniques.