We consider the problem of built-in test generation for synchronous sequential circuits. The proposed scheme leaves the circuit flip-flops unmodified, and thus allows at-speed test application. We introduce a uniform, parametrized structure for test pattern generation. By matching the parameters of the test pattern generator to the circuit-under-test, high fault coverage is achieved. In many cases, the fault coverage is equal to the fault coverage that can be achieved by deterministic test sequences. We also investigate a method to minimize the size of the test pattern generator, and study its effectiveness alone and in conjunction with the insertion of test-points.