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This paper presents two new, efficient solutions to the two-view, relative pose problem from three image point correspondences and one common reference direction. This three-plus-one problem can be used either as a substitute for the classic five-point algorithm, using a vanishing point for the reference direction, or to make use of an inertial measurement unit commonly available on robots and mobile devices where the gravity vector becomes the reference direction. We provide a simple, closed-form solution and a solution based on algebraic geometry which offers numerical advantages. In addition, we introduce a new method for computing visual odometry with RANSAC and four point correspondences per hypothesis. In a set of real experiments, we demonstrate the power of our approach by comparing it to the five-point method in a hypothesize-and-test visual odometry setting.