In recent years, a number of visual servo control algorithms have been proposed. Most approaches try to solve the inherent problems of image-based and position-based servoing by partitioning the control between image and Cartesian spaces. However, partitioning of the control often causes the Cartesian path to become more complex, which might result in operation close to the joint limits. A solution to avoid the joint limits is to use a shortest-path approach, which avoids the limits in most cases. In this paper, two new shortest-path approaches to visual servoing are presented. First, a position-based approach is proposed that guarantees both shortest Cartesian trajectory and object visibility. Then, a variant is presented, which avoids the use of a 3D model of the target object by using homography based partial pose estimation.