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Objectives: Melanoma is the deadliest form of skin cancer, but it can be fully cured through early detection and treatment in99% of cases. Our aim was to develop a non-invasive machine learning system that can predict the thickness of a melanomalesion, which is a proxy for tumor progression, through dermoscopic images. This method can serve as a valuable tool inidentifying urgent cases for treatment. Methods: A modern convolutional neural network architecture (EfficientNet) wasused to construct a model capable of classifying dermoscopic images of melanoma lesions into three distinct categories basedon thickness. We incorporated techniques to reduce the impact of an imbalanced training dataset, enhanced the generalizationcapacity of the model through image augmentation, and utilized five-fold cross-validation to produce more reliablemetrics. Results: Our method achieved 71% balanced accuracy for three-way classification when trained on a small publicdataset of 247 melanoma images. We also presented performance projections for larger training datasets. Conclusions: Ourmodel represents a new state-of-the-art method for classifying melanoma thicknesses. Performance can be further optimizedby expanding training datasets and utilizing model ensembles. We have shown that earlier claims of higher performance weremistaken due to data leakage during the evaluation process.