Covariant parsimony pressure is a theoretically motivated method primarily aimed to control bloat. In this contribution we describe an adaptive method to control covariant parsimony pressure that is aimed to reduce overfitting in symbolic regression. The method is based on the assumption that overfitting can be reduced by controlling the evolution of program length. Additionally, we propose an overfitting detection criterion that is based on the correlation of the fitness values on the training set and a validation set of all models in the population. The proposed method uses covariant parsimony pressure to decrease the average program length when overfitting occurs and allows an increase of the average program length in the absence of overfitting. The proposed approach is applied on two real world datasets. The experimental results show that the correlation of training and validation fitness can be used as an indicator for overfitting and that the proposed method of covariant parsimony pressure adaption alleviates overfitting in symbolic regression experiments with the two datasets.