We consider issues related to the testing of a random-logic legacy core embedded in user-defined logic. We assume that the only information available about the core is its test set. We develop a model for the core and the surrounding logic and provide procedures for testing the core and its surrounding logic under this model without adding design-for-testability (DFT) logic (such as a test wrapper). The procedures maximize the information extracted from the test set given for the core in order to maximize the fault coverage achieved without DFT. This maximizes the ability to test the circuit at-speed through its functional paths that go through cores and user-defined logic. We also describe DFT insertion procedures. The core and the surrounding logic are considered simultaneously during DFT insertion to minimize the amount of DFT logic required. We consider combinational logic (corresponding to full-scan) as well as sequential logic.