Recent observations of ridge bathymetry suggest magmatic segmentation at fast- and intermediate-spreading centers is linked to the migration of the spreading axis over the mantle. At fast- and intermediate-spreading centers, Carbotte et al. (2004) observed that leading segments, those that are offset in the direction of ridge migration, are typically shallower (interpreted to be magmatically robust) relative to trailing segments across first- and second-order discontinuities. The model set forth for this correlation invokes asymmetrical mantle upwelling in response to the absolute motion of the ridge axis and the entrainment of melt from across discontinuities. In this investigation, differences in ridge axis depth across first- and second-order discontinuities are examined within the context of absolute plate motions for portions of the slow-spreading Mid-Atlantic Ridge (MAR 22--36¿N and 25--35¿S latitude), intermediate-spreading Gal¿pagos Spreading Center (GSC 83--98¿W), and intermediate-spreading South East Indian Ridge (SEIR 77--114¿E). Portions of each of these areas display chemical and/or physical anomalies resulting from hot spot--ridge interaction. Along non--hot spot--influenced sections of intermediate-spreading ridges, leading segments coincide with shallower segments across 72% of the first- and second-order discontinuities (86% of transform faults and 55% of second-order discontinuities). Depth asymmetries vary with ridge offset length, with maximum asymmetries for ridge offset lengths of 50--100 km. A weaker correlation is observed between ridge migration direction and ridge morphology at the slow-spreading MAR, where leading segments are shallower across ~60% of first- and second-order discontinuities. For hot spot--influenced spreading centers, hot spot proximity dominates ridge morphology at intermediate-spreading centers, but it is not a consistent predictor of axial depth asymmetries at slow-spreading centers. This spreading-rate-dependent influence of ridge migration and hot spot proximity on axial morphology may reflect a more limited entrainment of melt from across slow-spreading discontinuities due to the predominance of three-dimensional upwelling and melt focusing to segment centers.