Greedy algorithms for the construction of software interaction test suites are studied. A framework is developed to evaluate a large class of greedy methods that build suites one test at a time. Within this framework are many instantiations of greedy methods generalizing those in the literature. Greedy algorithms are popular when the time for test suite construction is of paramount concern. We focus on the size of the test suite produced by each instantiation. Experiments are analyzed using statistical techniques to determine the importance of the implementation decisions within the framework. This framework provides a platform for optimizing the accuracy and speed of "one-test-at-a-time" greedy methods.