Accelerated destructive degradation tests (ADDTs) are widely used in manufacturing industries to obtain timely product reliability information, especially in applications where few or no failures are expected under use conditions in tests of practical length. An ADDT plan specifies the test conditions of accelerating variables, running time, and the corresponding allocation of test units to each condition. Usually, variables such as temperature, voltage, or pressure can be used as accelerating variables to accelerate degradation of a product. For some applications, however, tests at high-stress test conditions would result in more than one type of failure for test units, called competing risk problems. Careful test planning is important for efficient use of limited resources: test time, test units, and test facilities. This paper describes methods to find unconstrained and constrained optimum test plans for competing risk applications under a given test optimization criterion, such as minimizing the large-sample approximate variance of a failure-time distribution quantile at use conditions. A modified general equivalence theorem (GET) is used to verify the optimality of a given ADDT plan. Generally, an optimum test plan provides insight for constructing a good compromise test plan which tends to be more robust and practical. Monte Carlo simulations are used to provide visualization of the results that might be obtained from given test plans. The methods are illustrated with an application for an adhesive bond.