This paper examines the predictive capacity of two Grey Systems Forecasting models. The original Grey GM(1,1) Forecasting model, introduced by Deng [1] [2] together with an improved Grey GM(1,1) model proposed by Ji et al. [3] are used to forecast medical tourism demand for Bermuda. The paper also introduces a quasi-optimization method for the optimization of the alpha (weight) parameter. Five steps ahead out-of-sample forecasts are produced after estimating the models using four data points. The results indicate that the optimization of the alpha parameter substantially improves the predictive accuracy of the models; reducing the five steps ahead out-of-sample Mean Absolute Percentage Error from roughly 7% to roughly 3.80% across the two models. Largely, the forecasting approaches demonstrate significant potential for use as an alternative to the traditional forecasting methods in circumstances where substantial amounts of high-quality data are not available.