Well-constrained hypocenters (latitude, longitude, depth, and origin time) are required for nearly all studies that use earthquake data. We have examined the theoretical basis behind some of the widely accepted “rules of thumb” for obtaining accurate hypocenter estimates that pertain to the use of S phases and illustrate, in a variety of ways, why and when these “rules” are applicable. Results of experiments done for this study show that epicentral estimates (latitude and longitude) are typically far more robust with respect to data inadequacies; therefore, only examples illustrating the relationship between S phase arrival time data and focal depth and origin time estimates are presented. Most methods used to determine earthquake hypocenters are based on iterative, linearized, least-squares algorithms. Standard errors associated with hypocenter parameters are calculated assuming the data errors may be correctly described by a Gaussian distribution. We examine the influence of S-phase arrival time data on such algorithms by using the program HYPOINVERSE with synthetic datasets. Least-squares hypocenter determination algorithms have several shortcomings: solutions may be highly dependent on starting hypocenters, linearization and the assumption that data errors follow a Gaussian distribution may not be appropriate, and depth/origin time trade-offs are not readily apparent. These shortcomings can lead to biased hypocenter estimates and standard errors that do not always represent the true error. To illustrate the constraint provided by S-phase data on hypocenters determined without some of these potential problems, we also show examples of hypocenter estimates derived using a probabilistic approach that does not require linearization. We conclude that a correctly timed S phase recorded within about 1.4 focal depth's distance from the epicenter can be a powerful constraint on focal depth. Furthermore, we demonstrate that even a single incorrectly timed S phase can result in depth estimates and associated measures of uncertainty that are significantly incorrect.