We present our analysis of a fully sampled, high resolution dust extinction map of the Barnard 59 complex in the Pipe Nebula. The map was constructed with the infrared color excess technique applied to a photometric catalog that combines data from both ground and space based observations. The map resolves for the first time the high density center of the main core in the complex, which is associated with the formation of a small cluster of stars. We found that the central core in Barnard 59 shows an unexpected lack of significant substructure consisting of only two significant fragments. Overall, the material appears to be consistent with being a single, large core with a density profile that can be well fit by a King model. A series of NH₃ pointed observations toward the high column density center of the core appear to show that the core is still thermally dominated, with subsonic non-thermal motions. The stars in the cluster could be providing feedback to support the core against collapse, but the relatively narrow radio lines suggest that an additional source of support, for example, a magnetic field, may be required to stabilize the core. Outside the central core our observations reveal the structure of peripheral cores and resolve an extended filament into a handful of significant substructures whose spacing and masses appear to be consistent with Jeans fragmentation.