This paper presents a new approximate algorithm for image reconstruction with cone-beam spiral CT data at relatively small cone-angles. Based on the algorithm of Wang et al. [3], our method combines a special complementary interpolation with filtered backprojection. The presented algorithm has three main advantages over Wang's algorithm: 1) It overcomes the pitch limitation of Wang's algorithm. 2) It significantly improves z-resolution when suitable sampling schemes are applied. 3) It avoids the waste of applied radiation dose inherent to Wang's algorithm, Usage of the total applied dose is an important requirement in medical imaging. Our method has been implemented on a standard workstation. Reconstructions of computer-simulated data of different phantoms, assuming sampling conditions and image quality requirements typical to medical CT, show encouraging results.