Empirical evidence suggests that a monetary shock induces the exchange rate to overshoot its long-run level. The estimated magnitude and timing of the overshooting, however, varies across studies. This paper generates delayed overshooting in a new Keynesian model of a small open economy by incorporating incomplete information about the true nature of the monetary shock. The framework allows for a sensitivity analysis of the overshooting result to underlying structural parameters. It is shown that policy objectives and measures of the economy's sensitivity to exchange rate dynamic affect the timing and magnitude of the overshooting in a predictable manner, suggesting a possible rationale for the cross-study variation of the delayed overshooting Phenomenon.