We analyse the global structure of the old stellar discs in 34 edge-on spiral galaxies. The radial and vertical exponential scale parameters of the discs are obtained by applying an improved two-dimensional decomposition technique to our I-band photometry. We find a clear increase in the disc scaleheight with maximum rotational velocity, in accordance with observations of the stellar velocity dispersions in galaxy discs. The range and maximum of the intrinsic flattening of the disc light seem to increase with both maximum rotational velocity and total HI mass. We use the disc flattening to estimate the disc contribution to the maximum rotational velocity, resulting in an average of 57+-22 percent. The disc light distributions are further investigated for the presence of radial truncations. We find that the radial light distributions of at least 20 spirals are truncated, corresponding to 60 percent of the sample. For small scalelength spirals, which are the most numerous in the local Universe, the results suggest that the average ratio of disc truncation radius to disc scalelength is at least four.