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State-of-the-art value predictors either use control-flow context or data context to predict values. Predictors based on control-flow context use branch histories to remember past values, but these predictors require lengthy histories to predict anything other than constant and strided values. Predictors that use data context---also known as Finite Context Method (FCM) predictors---use a history of past values to predict a broader class of values, but such predictors achieve low coverage due to long training times, and they can become complex due to speculative value histories. We observe that the combination of branch and value history provides better predictability than the use of each history separately because it can predict values in control-dependent sequences of values. Furthermore, the combination improves training time by enabling accurate predictions to be made with shorter history, and it simplifies the hardware design by removing the need for speculative value histories. Based on these observations, we propose a new unlimited budget value predictor, Heterogeneous-Context Value Predictor (HCVP), that when hybridized with E-Stride, achieves a geometric mean IPC of 3.88 on the 135 public traces, as compared to 3.81 for the current leader of the Championship Value Prediction.