Many useful test case construction methods that are based on important aspects of the specification have been proposed in the literature. A comprehensive test suite thus obtained is often very large and yet is non-redundant with respect to the aspects identified from the specification. This paper addresses the problem of selecting a subset of test cases from such a test suite. We propose the use of white box criteria to select test cases from the initial black-box-generated test suite. We illustrate our ideas with examples and demonstrate the viability and benefits of our approach by means of a case study.