This conference paper was presented at BCS Displays Group - Visualisation and Modelling conference at the University of Leeds, 6-7 December 1995. Jack Bresenham attended the conference and liked the work because of the relevance of ray sampling adapted to reduce calculations by employing bilinear interpolation in the face rather than trilinear interpolation within a cube. I wrote it up more fully in my thesis, and it was published as a book chapter in Earnshaw, Jones and Vince (eds.), Visualization and Modeling, (London : Academic Press, 1997), 253-286. See Acceleration Techniques for Volume Rendering for that and Professor Mark W. Jones Publications List for further publications. Abstract In this paper we present a method for accelerating volume rendering by judicious choice of the sample stepping distance. This distance is taken for convenience to be 1 unit in the standard algorithm, but the algorithm can be accelerated by adapting the distance to the view direction. Advantage can be taken of the fact that samples occur only on cube faces, and realistically the computational cost of the volume rendering algorithm is reduced by 50\%, with very little image degradation. This method achieves an excellent balance between the image quality and computation time. The method involves very little extra computation to initiate, and works for arbitrary viewing directions.