Mmax the maximum magnitude earthquake that a fault is likely to suffer, plays an important role in earthquake hazard estimation. Although observational evidence summarized in plots of characteristic earthquake magnitude (Mchar) versus fault length indicate that smaller faults produce lower magnitude events, an argument has been made that any fault regardless of its length should have Mmax near magnitude 8. The rationale for this argument charges that the contrary observational evidence stems from historical catalogs of limited extent and that it largely excludes nonconventional earthquakes in which several short and apparently disconnected fault segments fail simultaneously. This article addresses Mmax using computer models of rupture on faults of various strengths and configurations. Computer models have advantages in that (a) Mmax earthquakes always can be generated by forcing complete stress drop on fully stressed faults, thus avoiding the limitations of short historical catalogs, and (b) the circumstances necessary for the failure of several segments to contribute to a large Mmax can be investigated quantitatively. I find that for a strikeslip California environment, it is physically unlikely for an M 8 event to break less than 300 to 400 km of fault. Were this M 8 rupture to occur on as few as five independent segments, shear strength of the participating faults would have to be raised to implausible levels. If the fault segments are not independent and their coseismic stress fields interact, then amplifications in slip are possible without drastic increase in strength. The range of fault geometries where strong interactions and amplifications of stress occur, however, is very restricted, and discontinuous faults separated by even 5% of their length act more or less independently. Mmax earthquakes breading realistic-looking distributions of discontinuous faults rarely are more than 0.1-magnitude unit bigger than would be predicted from a moment summation based on the characteristic magnitude Mchar of each of the individual faults. A prudent course in hazard analysis differentiates Mmax from Mchar allowing Mmax to be 0.2 to 0.3 units larger than Mchar but not automatically equal to 8.