Disparity tuning of visual cells in the brain depends on the structure of their binocular receptive fields (RFs). Freeman and coworkers have found that binocular RFs of a typical simple cell can be quantitatively described by two Gabor functions with the same gaussian envelope but different phase parameters in the sinusoidal modulations (Freeman and Ohzawa 1990). This phase-parameter-based RF description has recently been questioned by Wagner and Frost (1993) based on their identification of a so-called characteristic disparity (CD) in some cells' disparity tuning curves. They concluded that their data favor the traditional binocular RF model, which assumes an overall positional shift between a cell's left and right RFs. Here we set to resolve this issue by studying the dependence of cells' disparity tuning on their underlying RF structures through mathematical analyses and computer simulations. We model the disparity tuning curves in Wagner and Frost's experiments and demonstrate that the mere existence of approximate CDs in real cells cannot be used to distinguish the phase-parameter-based RF description from the traditional position-shift-based RF description. Specifically, we found that model simple cells with either type of RF description do not have a CD. Model complex cells with the position-shift-based RF description have a precise CD, and those with the phase-parameter-based RF description have an approximate CD. We also suggest methods for correctly distinguishing the two types of RF descriptions. A hybrid of the two RF models may be required to fit the behavior of some real cells, and we show how to determine the relative contributions of the two RF models.