A recently-developed miniaturized disk-bend test (MDBT) has been successfully used to evaluate the mechanical properties of a variety of materials, using specimens 3 mm in diameter. The load is applied either by a solid ball (the ball-on-ring (BOR) mode), or by a hollow cylinder (the ring-on-ring (ROR) mode). We have reproduced the yield stresses of ordered intermetallic compounds and the fracture toughnesses of several ceramics using analytical solutions to the equations of elasticity theory. Despite this success there are several curious features involved in the analysis of data, for example, in previous tests conducted in the BOR mode correct values of the yield stress were obtained using the equations appropriate to clamped specimens, whether or not they were actually clamped in the test fixture. We show that this is ubiquitous to tests in the BOR mode, and does not arise because of frictional constraints at the supporting ring. We have also completed a thorough evaluation of testing in the ROR mode, in which the yield stresses of cold-rolled or annealed AISI type 302 stainless steel were measured using various combinations of specimen thickness and radii of the loading and supporting rings, and compared to those of tensile specimens machined from the same material. The most accurate and reproducible measurements of the yield strength were obtained for specific combinations of specimen thickness and geometry of the apparatus. We describe these conditions and demonstrate that they provide values that are always within 10% of the tensile results. The errors induced by potential misalignments in the MDBT are also discussed, and are shown to cause no more than a 5% deviation in the measured yield stress.