A common problem in exploratory factor analysis is how many factors need to be extracted from a particular data set. We propose a new method for selecting the number of major common factors: the Hull method, which aims to find a model with an optimal balance between model fit and number of parameters. We examine the performance of the method in an extensive simulation study in which the simulated data are based on major and minor factors. The study compares the method with four other methods such as parallel analysis and the minimum average partial test, which were selected because they have been proven to perform well and/or they are frequently used in applied research. The Hull method outperformed all four methods at recovering the correct number of major factors. Its usefulness was further illustrated by its assessment of the dimensionality of the Five-Factor Personality Inventory (Hendriks, Hofstee, & De Raad, 1999). This inventory has 100 items, and the typical methods for assessing dimensionality prove to be useless: the large number of factors they suggest has no theoretical justification. The Hull method, however, suggested retaining the number of factors that the theoretical background to the inventory actually proposes. (Contains 3 tables and 1 figure.)