A method of predicting sphere diameter distributions from chord size data is presented and evaluated. This is the probability apportioning method (PAM2) and is significantly improved on a previous presentation. It assumes that the particles or droplets are near spherical and cut randomly by a sensor. For an assumed particle diameter distribution, Bayes' theorem is used to calculate hit probabilities for each particle diameter. The diameter distribution is then recalculated and the process is repeated until there is no significant further change. Using numerical simulations, PAM2 is shown to be quite accurate and robust for a number of different types of size distribution.