We compare a design innovation of an elliptically framed tip-tilt optical tracker with an existing circularly framed tracker for the Navy Precision Optical Interferometer. The tracker stabilizes a 12.5 cm stellar beam on a target hundreds of meters away and requires an increase in operational frequency. We reduced mass and size by integrating an elliptical mirror as one of the rotating components, which eliminated a rotating frame. We used the same materials as the existing tracker; however, light-weighted both the aluminum frame and Zerodur® mirror. We generated a computer-aided design model, converted it into a finite element model and performed modal analysis on two load cases. In load case 1, we tied down three points on the bottom surface of the tracker corresponding to the tie-down points of the comparison tracker. This reveals a first mode (lowest) frequency of 140 Hz, a factor of two over the baseline tracker's first mode frequency of 67 Hz. In load case 2, we constrained four additional points inboard of the corners of the tracker base, for a total of seven tie-downs, simulating a firmly bolted and secured mount. The first mode of vibration for this case is 211 Hz, an increase over load case 1 by a factor of 1.5 and more than three times the fundamental frequency of the existing tracker. We conclude that these geometrical changes with the additional tie-down bolts are a viable solution path forward to improve steering speed and recommend a continuation with this effort.