The morphology of turbidite slope channels and the distribution of reservoir and nonreservoir facies within them are commonly complicated by the interaction of the channels with the development of structurally induced topography. The pattern of channel response may be dictated by the timing of structural growth related to channel development, the size and shape of the structures, the orientation of the structure to depositional dip, and the erosional power of the channels. Several three-dimensional seismic data sets have been examined from passive margins deformed by gravity-driven tectonics to investigate the range of responses that large, third-order erosional channel complex systems can show to slope topography. The examples are examined with respect to timing of the growth-related seabed topography versus timing of channel formation and the erosive power of the flows within the channel. Structures that develop aerially limited sea-floor topography, which predates channel development, cause turbidite channels to take a moderate diversion as they traverse the slope. Where similar structures are more laterally extensive, channels may take extreme diversions, commonly kilometers along slope before continuing down the regional slope. When the erosion of the flows is strong enough and can overcome the rate of growth of the structure, channels can continue to incise across the growing structure. If the rate of growth of the structure is higher, the channel systems shift systematically sideways to avoid the rising topography. The style of the sedimentation-topography interaction has a strong but commonly subtle effect on the geometry, internal stratigraphic architecture, and nature and distribution of the facies deposited within and around the channels.