The parabolic technique previously devised to project geological assessments of undiscovered resources of conventional oil was modified to determine the date of occurrence of assumed values of the peak in world conventional oil production. The objective was to check the self-consistency of a range of typical values for the peak with the timing often quoted in the energy literature. Four cases for the unconstrained peak were chosen and the results were compared with those from a Reference Case that appeared in an earlier paper which was based upon the 1990 World Resources Assessment of the U.S. Geological Survey. The quantity of oil expected to be produced after 2003 was also calculated for each case.The four cases chosen were: A - 85 million barrels per day (31.03 gigabarrels per year) with the peak found to occur in 2022.2; B - 90 mbbls/day (32.85 GB/Y) with the peak in 2031.8; C - 95 mbbls/day (34.68 GB/Y) with the peak in 2041.3; and D - 100 mbbls/day (36.50 GB/Y) with the peak in 2050.6. The timing of the peak was found to vary linearly with its value in the parabolic model. The quantity of oil expected to be produced after 2003 was also found to be approximately linear with the date of the peak. These values were so high that it is unlikely that the peak in the world production of conventional oil will exceed 90 million barrels per day. The Reference Case calculated from the resource assessment in the earlier note predicts the peak to be in 2015.4 which seems more probable.