Delivery systems for delivering and deploying expandable intraluminal medical devices within a body vessel are provided. A portion of the delivery system that includes the expandable intraluminal medical device orients itself about an axis based on characteristics of the body vessel, such as the relative orientation of major and minor axes of the vessel. This allows the intraluminal medical device to be deployed in the vessel in a desired orientation relative to the vessel. Embodiments can be used with any suitable intraluminal medical device, including valve devices, stents, drug-coated stents, filters, and other suitable devices. Methods of delivering and deploying intraluminal medical devices are also described.