We are investigating on-line model-based test generation from non-deterministic output-observable Input/Output Extended Finite State Machine (I/O EFSM) models of Systems Under Test (SUTs). We propose a novel constraint-based heuristic approach (Heuristic Reactive Planning Tester (xRPT)) for on-line conformance testing non-deterministic SUTs. An indicative feature of xRPT is the capability of making reasonable decisions for achieving the test goals in the on-line testing process by using the results of off-line bounded static reachability analysis based on the SUT model and test goal specification. We present xRPT in detail and make performance comparison with other existing search strategies and approaches on examples with varying complexity.