Simultaneously recovering the camera pose and correspondences between a set of 2D-image and 3D-model points is a difficult problem, especially when the 2D-3D matches cannot be established based on appearance only. The problem becomes even more challenging when input images are acquired with an uncalibrated camera with varying zoom, which yields strong ambiguities between translation and focal length. We present a solution to this problem using only geometrical information. Our approach owes its robustness to an initial stage in which the joint pose and focal length solution space is split into several Gaussian regions. At runtime, each of these regions is explored using an hypothesize-and-test approach, in which the potential number of 2D-3D matches is progressively reduced using informed search through Kalman updates, iteratively refining the pose and focal length parameters. The technique is exhaustive but efficient, significantly improving previous methods in terms of robustness to outliers and noise.