The development of accurate and efficient algorithms for image reconstruction from helical cone-beam projections remains a subject of active research. In the last few years, a number of quasi-exact and exact algorithms have been developed. Among them, the Katsevich algorithms are of filtered backprojection type and thus possess computational advantages over other existing exact algorithms. In this work, we propose an alternative approach to reconstructing exactly an image from helical cone-beam projections. Based on this approach, we develop an algorithm that requires less data than do the existing quasi-exact and exact algorithms, including the Katsevich algorithms. Our proposed algorithm is also of filtered backprojection type with one-dimensional filtering performed along a PI-line in image space. Therefore, it is (at least) computationally as efficient as the Katsevich algorithms. We have performed a preliminary numerical study to demonstrate and validate the proposed algorithm using computer-simulation data. The implication of the proposed approach and algorithm appears to be significant in that they can naturally address the long object problem as well as the super-short scan problem and, most importantly, in that they provide the opportunity to reconstruct images within any selected region of interest from minimum data, allowing the use of detector with a reduced size, the selection of a minimum number of rotation angles and thus the reduction of radiation dose delivered to the imaged subject.