In this paper, we analyze new possibilities in predicting daily ranges, i.e. differences between daily high and low prices. We empirically assess efficiency gains in volatility estimation when using range-based estimators as opposed to simple daily ranges and explore the use of these more efficient volatility measures as predictors of daily ranges. The array of models used in this paper include the heterogeneous autoregressive model, conditional autoregressive ranges model and a vector error-correction model of daily highs and lows. Contrary to intuition, models based on co-integration of daily highs and lows fail to produce good quality out of sample forecasts of daily ranges. The best one-day-ahead daily ranges forecasts are produced by a realized range based HAR model with a GARCH volatility-of-volatility component.