The present paper describes new relationships which are in fact mostly very simple: Certain rates of buying are more or less constant across different brands and pack-sizes, and this holds for different product fields and for different lengths of time-period. These relationships have been established by searching for patterns which generalise. The findings may appear insufficiently statistical to gain instant acceptance from people used to more complicated kinds of results, and a selection of summary tables is therefore given. The relevance of the results to various aspects of brand-loyalty is clear, but both the practical and the theoretical implications require further work to bring out in detail. Since complex mathematical models are nowadays regarded as potentially useful, the simple results here should turn out to be even easier to use.