Consider the problem of spatial prediction of a random process from a spatial dataset. Global spatial-predictor selection provides a way to choose a single spatial predictor from a number of competing predictors. Instead, we consider local spatial-predictor selection at each spatial location in the domain of interest. This results in a hybrid predictor that could be considered global, since it takes the form of a combination of local predictors; we call this the locally selected spatial predictor. We pursue this idea here using the (empirical) deviance information as our criterion for (global and local) predictor selection. In a small simulation study, the relative performance of this combined predictor, relative to the individual predictors, is assessed.