The present invention is a system for efficiently generating test cases characterized by a linear range of integral values. A software testing tool which has been configured to generate test cases characterized by a linear range of integral values in accordance with the present invention can include a user interface coupled to a test case generator. The test case generator can be configured for range bounding for a range of integral values in a software application under test. In particular, the test case generator can include a halving module programmed to identify changes in response states in the software application under test evoked from input tokens having selected ones of the lengths defined within sub-ranges of a specified range of integral values.