Cancer accounts for a huge mortality rate due to its aggressiveness, colossal potential of metastasis, and heterogeneity (causing resistance against chemotherapy). Lung and colon cancers are among the most prevalent types of cancer around the globe that can occur in both males and females. Early and accurate diagnosis of these cancers can substantially improve the quality of treatment as well as the survival rate of cancer patients. We propose a highly accurate and computationally efficient model for the swift and accurate diagnosis of lung and colon cancers as an alternative to current cancer detection methods. In this study, a large dataset of lung and colon histopathology images was employed for training and the validation process. The dataset is comprised of 25000 histopathology images of lung and colon tissues equally divided into 5 classes. A pretrained neural network (AlexNet) was tuned by modifying the four of its layers before training it on the dataset. Initial classification results were promising for all classes of images except for one class with an overall accuracy of 89%. To improve the overall accuracy and keep the model computationally efficient, instead of implementing image enhancement techniques on the entire dataset, the quality of images of the underperforming class was improved by applying a contrast enhancement technique which is fairly simple and efficient. The implementation of the proposed methodology has not only improved the overall accuracy from 89% to 98.4% but has also proved computationally efficient.