The Katsevich algorithm is a breakthrough in the theoretically exact algorithms for helical cone beam computed tomography (CT). For future application in medical and industrial CT, determining how to implement it efficiently and accurately is the main task. We analyzed the slope law and intersection law of the k-lines, finding that the k-lines are not intersecting if the half-maximal fan angle (HMFA) is (numerical solution, so it is approximate) and that the helical pitch and HMFA determine the depth of parallelism of k-lines. Using an appropriate pitch and an HMFA that is , one can use a simplified Katsevich algorithm, whose filtration process can be done on the rows of the detector panel so that the preweighting, pre-rebinning, post-rebinning, and postweighting steps are all canceled. Simulation experiments show that the simplified algorithm can obtain highly precise images at a faster speed. Our results are intended to be valuable to those who are working on efficient implementations of the Katsevich-type algorithms.