We explore the use of a penalized complexity prior for the parameter regulating the variance of the measurement error in the covariates. We refer to area-level models that belong to the wider class of small-area models. Our proposal induces an increasing shrinkage towards the potential absence of measurement error as long as we add information through the inclusion of additional covariates. In this setting, we assume that a subset of covariates is measured with error, with a similar amplitude throughout the small areas. Our proposal aims to provide accurate estimates and, at the same time, to perform model selection. To this end, we implement a posterior predictive p-value procedure to discriminate among models. This is computationally easier than the more formal computation of the Bayes factor, which is particularly challenging in this context.