Forecasters often encounter situations in which the local pattern of a time series is not expected to persist over the forecasting horizon. Since exponential smoothing models emphasize recent behavior, their forecasts may not be appropriate over longer horizons. In this paper, we develop a new model in which the local trend line projected by exponential smoothing converges asymptotically to an assumed future long-run trend line, which might be an extension of a historical long-run trend line. The rapidity of convergence is governed by a parameter. A familiar example is an economic series exhibiting persistent long-run trend with cyclic variation. This new model is also useful in applying judgmental adjustments to a statistical forecast. For example, this new model can converge an exponential smoothing forecast to a judgment-imposed future trend line that represents – say – a 10% increase over the extrapolated trend. The accuracy of this new method will be compared (later – haven’t done this yet) to that of existing methods in forecasting a sample of cyclical series with long-run trends.