Iterative reconstruction algorithms for helical CT are presented. The algorithms are derived from two-dimensional reconstruction algorithms, by adapting the projector/backprojector to the helical orbit of the source, and by constraining the axial frequencies with a Gaussian sieve. Simulations have been carried out and the performance of the iterative algorithms is compared to that of filtered backprojection of synthetic (interpolated) two-dimensional sinograms. The iterative algorithms produce superior bias-noise curves. Axial resolution is superior, but disturbing edge-artefacts are introduced.