Volumes reconstructed by standard methods from single-slice helical computed tomography (CT) data have been shown to have noise levels that are highly nonuniform relative to those in conventional CT. These noise nonuniformities can affect low-contrast object detectability and have also been identified as the cause of the zebra artifacts that plague maximum intensity projection (MIP) images of such volumes. While these spatially variant noise levels have their root in the peculiarities of the helical scan geometry, there is also a strong dependence on the interpolation and reconstruction algorithms employed. In this paper, we seek to develop image reconstruction strategies that eliminate or reduce, at its source, the nonuniformity of noise levels in helical CT relative to that in conventional CT. We pursue two approaches, independently and in concert. We argue, and verify, that Fourier-based longitudinal interpolation approaches lead to more uniform noise ratios than do the standard 360LI and 180LI approaches. We also demonstrate that a Fourier-based fan-to-parallel rebinning algorithm, used as an alternative to fanbeam filtered backprojection for slice reconstruction, also leads to more uniform noise ratios, even when making use of the 180LI and 360LI interpolation approaches.