LTE test cases are standardized by 3GPP. They must be executed on every LTE-capable device model before commercial release. In this work, we examine the LTE testing practices in terms of completeness and efficiency. We discover that the standardized tests are incomplete in that a number of test cases related to multiple protocol interactions are missing. Our analysis also shows that, the isolated treatment of test cases, but not from the system perspective, incurs repetitive executions of test operations, thus resulting in testing inefficiencies. We thus make a case for a paradigm shift from ad hoc testing to a methodical approach to LTE testing. We follow a few guidelines from the LTE standards and propose an algorithmic approach to systematic testing. In the process, we address various challenges, provide complete list of test cases, and present the related algorithms. Our evaluation shows that, by eliminating repetitive operations, our new scheme reduces up to 70% of LTE testing steps. We also find 87 new, yet valid test cases that are not defined by the LTE standards.