We present a low-cost on-line test methodology for RTL controller-datapath pairs, based on the notion of path invariance. The fundamental observation supporting the proposed methodology is that the transparency behavior inherent in RTL components renders rich sources of invariance in a design. Furthermore, the algorithmic controller-datapath interaction provides additional sources of invariance. ? judicious selection and combination of modular transparency, based on the algorithm implemented by the controller-datapath pair, yields a powerful set of invariant paths. Such paths enable a simple, yet very efficient on-line test capability, achieving fault security in excess of 90% while keeping the hardware overhead below 40% on complicated, difficult to test, benchmarks.