Inverse kinematics for redundant robotic manipulators is typically computed using the pseudoinverse of the manipulator Jacobian. Though the pseudoinverse yields the most accurate minimum-norm joint velocity vector, it fails to prevent high joint velocities when the manipulator is in the neighborhood of singularities. The Singularity Robust Inverse (SRI), which arises from the Damped Least-Squares technique proves to be a better inverse kinematic solution than the pseudoinverse near singular configurations. The SRI computes damped joint velocities but causes some deviation of the end-effector from its planned trajectory. The SRI performs most satisfactorily when the damping factor, which represents the trade-off between the accuracy and feasibility of the computed solution is calculated optimally, i.e. it yields minimum deviation of the end-effector while ensuring the feasibility of the joint velocities at all points in the manipulator workspace. This work introduces a new method of computing the optimal damping factor. The SRI can also be used to optimize another sub-task criterion in addition to performing the main motion task and avoiding high joint velocities at singularities.