Recent work has demonstrated that Monte Carlo photon transport (MCPT) simulation is a practical and accurate dosimetry tool for characterizing brachytherapy dose distributions in the presence of complex three-dimensional (3D) geometries. Because of the steep dose gradients encountered in this application, the choice of estimation algorithm, i.e., the algorithm for extracting dose estimates from individual photon histories, is critical to ensure adequate spatial resolution and computational efficiency. While conventional MCPT dose estimation techniques are sufficiently accurate in many cases, they inevitably fail with the point of interest is located near media interfaces, since they require the point of interest to be contained by a region of homogeneous medium of several millimetres in diameter. This severely limits the domain of application of MCPT in brachytherapy dosimetry and prevents dose estimation at points such as those immediately behind lead shields contained in gynaecological applicators, or simulation of small intricately structured detector response. We have successfully adapted to an MCPT code a neutron-flux estimator, the one-more-collided flux estimator (OMCFE), which overcomes this problem. OMCFE is derived from the familiar next-flight estimation algorithm, and, through the use of a photon trajectory resampling scheme, does not require homogeneous media at the point of interest. it is therefore a true point-dose estimator. OMCFE was tested against a variety of one- and three-dimensional benchmark problems. These benchmarks included mono-energetic point sources of 30 and 600 keV, as well as a 3M model 6702 125I seed, a 137Cs tube, and an 192Ir seed in geometries approximating common brachytherapy dosimetric problems. OMCFE agrees closely with conventional MCPT dose estimation algorithms in solving these benchmark problems, while in many cases being much more efficient.