Because original high-quality non-market valuation studies can be expensive, perhaps prohibitively so, benefits transfer (BT) approaches are often used for valuing, e.g., the outputs of multifunctional agriculture. Here we focus on the use of BT functions, a preferred method, and address an under-appreciated problem – variable selection uncertainty – and demonstrate a conceptually superior method of resolving it. We show that the standard method of value-function BT, using the full estimated model, may generate BT values that are too sensitive to insignificant variables, whereas models reduced by backward elimination of insignificant variables pay no attention to insignificant variables that may in fact have some influence on values. Rather than searching for the best single model for BT, Bayesian model averaging (BMA) is attentive to all of the variables that are a priori relevant, but uses posterior model probabilities to give systematically lower weight to less significant variables. We estimate a full value model for wetlands in the US, and then calculate BT values from the full model, a reduced model, and by BMA. Variable selection uncertainty is exemplified by regional variables for wetland location. Predicted values from the full model are quite sensitive to region; reduced models pay no attention to regional variables; and the BMA predictions are attentive to region but give it relatively low weight. However, the suite of insignificant RHS variables, taken together, have non-trivial influence on BT values. BMA predicted values, like values from reduced models, have much narrower confidence intervals than values calculated from the full model.