The use of the average or maximum grain size, G, in G-tensile strength, sigma, relations and the resultant character of the sigma-G(-1/2) plots have been considered. Experimental and literature data (mainly at 22 degrees C) show that using the size of exaggerated grains in Al2O3, beta-Al2O3, B4C, SiC, Si3N4 and probably TiO2 (i.e, mainly non-cubic materials), is appropriate, provided such grains are the source of failure and are larger than or equal to the flaw size, which is most probable at intermediate G, otherwise an average G, G(a), is appropriate. Larger grains or clusters of larger grains do not always act as fracture origins, because associated flaws, mainly cracks (e.g. from machining) or pores are required. G(a) was found to be appropriate for materials (e.g. MgO, Y2O3, ZrO2 and MgAl2O4) not typically having exaggerated grains. The slopes of the larger and finer G branches of the sigma-G(-1/2) plots are shown to be less than for polycrystalline K-IC and more than 0, respectively, contrary to assertions of other workers using maximum G, G(m). The latter slope indicates that the R-curve effects and related mechanisms have much more limited effects on sigma than is commonly recognized. Better measurement and characterization needs are identified, i.e. (1) basic consistency between sigma and G values (violated in the past use of G(m)), and (2) addressing the spatial distribution of larger grains and other defects, e.g. via fractography. Use of an average (possibly weighted) grain diameter for G instead of a linear intercept, is recommended.