In uniform multiprocessor platforms, the various processors comprising the multiprocessor platform may have different computing capacities. The focus of this paper is the design of efficient tests for determining whether the Earliest Deadline First Scheduling Algorithm (EDF) can successfully schedule a given real-time task system to meet all deadlines upon a specified uniform multiprocessor platform. Upon uniform multiprocessor platforms, we show that it is often far easier (from a computational complexity perspective) to determine feasibility than it is to check for EDF-schedulability. In designing an EDF-schedulability test for uniform multiprocessors, therefore, our approach is as follows: for a given uniform multiprocessor platform, we attempt to efficiently identify all those uniform multiprocessor platforms such that any real-time instance feasible upon these platforms is guaranteed to be EDF-schedulable upon the platform under consideration. EDF-schedulability upon the given platform can then be determined by ascertaining whether the real-time system is feasible upon any of these platforms.