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Chest X-rays have been found to be very promising for assessing COVID-19 patients, especially for resolving emergency-department and urgent-care-center overcapacity. Deep-learning (DL) methods in artificial intelligence (AI) play a dominant role as high-performance classifiers in the detection of the disease using chest X-rays. While many new DL models have been being developed for this purpose, this study aimed to investigate the fine tuning of pretrained convolutional neural networks (CNNs) for the classification of COVID-19 using chest X-rays. Three pretrained CNNs, which are AlexNet, GoogleNet, and SqueezeNet, were selected and fine-tuned without data augmentation to carry out 2-class and 3-class classification tasks using 3 public chest X-ray databases. In comparison with other recently developed DL models, the 3 pretrained CNNs achieved very high classification results in terms of accuracy, sensitivity, specificity, precision, F1 score, and area under the receiver-operating-characteristic curve. AlexNet, GoogleNet, and SqueezeNet require the least training time among pretrained DL models, but with suitable selection of training parameters, excellent classification results can be achieved without data augmentation by these networks. The findings contribute to the urgent need for harnessing the pandemic by facilitating the deployment of AI tools that are fully automated and readily available in the public domain for rapid implementation.