Automated diagnosis of tuberculosis (TB) from chest X-Rays (CXR) has been tackled with either hand-crafted algorithms or machine learning approaches such as support vector machines (SVMs) and convolutional neural networks (CNNs). Most deep neural network applied to the task of tuberculosis diagnosis have been adapted from natural image classification. These models have a large number of parameters as well as high hardware requirements, which makes them prone to overfitting and harder to deploy in mobile settings. We propose a simple convolutional neural network optimized for the problem which is faster and more efficient than previous models but preserves their accuracy. Moreover, the visualization capabilities of CNNs have not been fully investigated. We test saliency maps and grad-CAMs as tuberculosis visualization methods, and discuss them from a radiological perspective.