In this paper, we introduce the concept of tunable visual features for moments based visual servoing schemes. The main contribution of this work is the introduction of tunable shift points along with some effective methods to tune them. We propose two different metrics: the first metric ensures optimal response of the control to errors in the image space and the second metric ensures orthogonality between the interaction matrix components (vectors) related to the control of x and y rotational motions. With the proposed method, it is possible to design moment invariants-based visual features whose interaction matrix is always non-singular for any desired pose (parallel or non-parallel). Thus, this work makes a significant contribution to the difficult problem of controlling the rotational motions around the x and y axes, when all the 6dof are involved. Two case studies are presented to demonstrate the validity of the proposed ideas. Results from each case are then used to design a moment invariants-based visual feature. This visual feature is used for visual servoing with a symmetrical object using binary moments and a free- form planar target using photometric moments.