Chest radiographs are among the most frequently acquired images in radiology and are often the subject of computer vision research. However, most of the models used to classify chest radiographs are derived from openly available deep neural networks, trained on large image datasets. These datasets differ from chest radiographs in that they are mostly color images and have substantially more labels. Therefore, very deep convolutional neural networks (CNN) designed for ImageNet and often representing more complex relationships, might not be required for the comparably simpler task of classifying medical image data. Sixteen different architectures of CNN were compared regarding the classification performance on two openly available datasets, the CheXpert and COVID-19 Image Data Collection. Areas under the receiver operating characteristics curves (AUROC) between 0.83 and 0.89 could be achieved on the CheXpert dataset. On the COVID-19 Image Data Collection, all models showed an excellent ability to detect COVID-19 and non-COVID pneumonia with AUROC values between 0.983 and 0.998. It could be observed, that more shallow networks may achieve results comparable to their deeper and more complex counterparts with shorter training times, enabling classification performances on medical image data close to the state-of-the-art methods even when using limited hardware.