MOTIVATION: Methods that estimate the quality of a 3D protein structure model in absence of an experimental reference structure are crucial to determine a model's utility and potential applications. Single model methods assess individual models whereas consensus methods require an ensemble of models as input. In this work, we extend the single model composite score QMEAN that employs statistical potentials of mean force and agreement terms by introducing a consensus-based distance constraint (DisCo) score. RESULTS: DisCo exploits distance distributions from experimentally determined protein structures that are homologous to the model being assessed. Feed-forward neural networks are trained to adaptively weigh contributions by the multi-template DisCo score and classical single model QMEAN parameters. The result is the composite score QMEANDisCo, which combines the accuracy of consensus methods with the broad applicability of single model approaches. We also demonstrate that, despite being the de-facto standard for structure prediction benchmarking, CASP models are not the ideal data source to train predictive methods for model quality estimation. For performance assessment, QMEANDisCo is continuously benchmarked within the CAMEO project and participated in CASP13. For both, it ranks among the top performers and excels with low response times. AVAILABILITY AND IMPLEMENTATION: QMEANDisCo is available as web-server at https://swissmodel.expasy.org/qmean. The source code can be downloaded from https://git.scicore.unibas.ch/schwede/QMEAN. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.