Fatigue crack-initiation sites in Ti–6Al–2Sn–4Zr–6Mo (Ti–6–2–4–6), an α+β titanium alloy used in turbine engine applications, were characterized with emphasis on distinguishing the microstructural neighborhoods and mechanisms that produce the life-limiting failures vs. those that promote the mean-lifetime behavior. The characterization methods included quantitative tilt fractography, focused ion beam milling across crack-initiation facets, and electron backscattered diffraction analysis. The motivation for discerning between the life-limiting and the mean-dominating crack-initiation microstructural neighborhoods stemmed from the previously developed understanding that the mean and the life-limiting behaviors respond differently to stress level (and many other variables), leading to an increasing separation between the two subpopulations as the stress level is decreased, thereby increasing the variability in lifetime. The different rates of response of the two behaviors was found to arise because the life-limiting mechanism was dominated by the crack-growth lifetime, with microstructural-scale crack-initiation occurring within the first few fatigue cycles, whereas the mean behavior was increasingly dominated by the crack-initiation lifetime as the stress level was decreased. Representative specimens for 2-D characterization of crack-initiation neighborhoods were selected from life-limiting and mean-dominating populations generated by fatigue tests on a duplex α+β phase microstructure of Ti–6–2–4–6 under a narrow range of applied stress amplitudes. A compilation of data on the crack-initiation facet and the neighborhood of the faceted grain from multiple specimens pointed to at least four categories of critical microstructural configurations, each representing a set of necessary (but perhaps not sufficient) conditions for crack-initiation in this alloy. Based on this characterization, a hypothesis for the life-limiting fatigue behavior is presented. The hypothesis invokes the concept of hierarchy of fatigue deformation heterogeneities, which is suggested to develop within the first few fatigue cycles. The deformation heterogeneity is suggested to be linked to the underlying randomness and hierarchy in the microstructural arrangements. This hypothesis appears to explain the occurrence of crack-growth-lifetime-dominated, life-limiting failures in the regime of high-cycle fatigue, as shown in this study, and suggests a probability of occurrence of such failures even in the very-high-cycle fatigue regime, although with diminishing probability as the stress level is decreased.