Specialists may gauge the severity of sickle cell disease crisis by quantifying the number of abnormal-looking and sickle-shaped erythrocytes in blood smears. State-of-the-art integral geometry-based descriptors for automatic classification of erythrocytes as normal cells, sickle cells or cells with other deformations have achieved excellent results. Unfortunately, they are computationally expensive, requiring powerful desktop computers and a great deal of memory to run. We propose two new integral geometry-based descriptors for the shape of erythrocytes. Like state-of-the-art techniques, the overall sensitivity of our solutions is above 94%. Nevertheless, our descriptors are designed to avoid a great amount of computation in comparison to similar solutions and to present a lower memory footprint. Our descriptors offer a high specificity of normal cells and a high sensitivity of deformed cells, making them a good alternative in clinical applications.