Pose estimation of 3-D objects based on monocular computer vision is an ill-posed problem. To ease matters a model-based approach can be applied. Such an approach usually relies on iterating when matching the model and the image data. In this paper we estimate the 3-D pose of a human arm from a monocular image. To avoid the inherent problems when iterating, we apply an exhaustive matching strategy. To make this plausible, we reduce the size of the solution space through a very compact model representation of the arm and prune the solution space. The model is developed through a detailed investigation of the functionality and structure of the arm and the shoulder complex. The model consists of just two parameters and is based on the screw-axis representation together with image measurements. The pruning is achieved through kinematic constraints and it turns out that the solution space of the compact model can be pruned 97%97\% , on average. Altogether, the compact representation and the constraints reduce the solution space significantly and, therefore, allow for an exhaustive matching procedure. The approach is tested in a model-based silhouette framework, and tests show promising results.