Our laboratory is developing a high-resolution PET detector capable of providing depth-of-interaction information (dMiCE) by tailoring the light sharing between two adjacent detector elements. Each detector element in the prototype system has a 2×2 mm(2) cross section and is directly coupled to a micro-pixel avalanche photodiode (MAPD). In this setup the distribution of the ratio of light shared between two adjacent detector elements can be expressed as a function of the depth of interaction. The three-dimensional points of interaction of a coincidence pair of photons within the detector module is estimated by numerical calculation of an expectation of the points of interaction conditioned on the signals measured by the MAPDs (Bayesian estimate). This conditional expectation is computed from estimates of the probability density function of the light collection process and a model of the kinetics of photon interactions in the detector module. Our algorithm is capable of handling coincidences where each photon interacts any number of times within the detector module before being completely absorbed or escaping. In the case of multiple interactions our algorithm estimates the position of the first interaction for each of the coincidence photons.