An entity’s existence in an image can be depicted by the activity instantiation vector from a group of neurons (called capsule). Recently, multi-layered capsules, called CapsNet, have proven to be state-of-the-art for image classification tasks. This research utilizes the prowess of this algorithm to detect pneumonia from chest X-ray (CXR) images. Here, an entity in the CXR image can help determine if the patient (whose CXR is used) is suffering from pneumonia or not. A simple model of capsules (also known as Simple CapsNet) has provided results comparable to best Deep Learning models that had been used earlier. Subsequently, a combination of convolutions and capsules is used to obtain two models that outperform all models previously proposed. These models—Integration of convolutions with capsules (ICC) and Ensemble of convolutions with capsules (ECC)—detect pneumonia with a test accuracy of 95.33% and 95.90%, respectively. The latter model is studied in detail to obtain a variant called EnCC, where n = 3, 4, 8, 16. Here, the E4CC model works optimally and gives test accuracy of 96.36%. All these models had been trained, validated, and tested on 5857 images from Mendeley.