A computer model of the AFM pull-off process was used to test the Poisson method for calculating bond forces and to compare the Poisson and histogram methods of finding single-molecule bond-rupture forces. The Poisson method appeared to work well, producing accurate individual bond-rupture forces even in the presence of moderate to large amounts of different types of variations or noise, while the histogram method only produced good results at low noise levels, even with large sample sizes. Three cases were found where use of the Poisson model could lead to inaccurate measurement of individual bond forces, the most important being related to the bond-formation probability, which must be low (ideally <5%) for accurate results. The Johnson-Kendall-Roberts (JKR) continuum method was also examined. Poisson and JKR methods are not expected to produce similar results, but are complementary, and if used together may produce accurate measurements of both individual bond-rupture forces and bond-formation probabilities, even if neither method alone is successful.