We consider the problem of domain shift in analyses of brain MRI data. While many different datasets are publicly available, most algorithms are still trained on a single dataset and often suffer the problem of limited and unbalanced sample sizes. In this work, we propose a surprisingly simple strategy to reduce the impact of domain shift - caused by different data sources and processing pipelines - that typically occurs in cross-dataset analyses. We experimentally evaluate our approach on the problem of using volumetric features to distinguish neurodegenerative diseases and report results using three datasets in two practically relevant scenarios: (1) cross-dataset learning and (2) leveraging pre-trained classifiers across different datasets. We show that our adaptation technique enables both scenarios with performance close to the single-dataset case.