We present a versatile three-lens optical design to improve the overall compactness, efficiency, and robustness for optical tweezers based applications. The design, inspired by the Cooke-Triplet configuration, allows for continuous beam magnifications of 2-10×, and axial as well as lateral focal shifts can be realized without switching lenses or introducing optical aberrations. We quantify the beam quality and trapping stiffness and compare the Cooke-Triplet design with the commonly used double Kepler design through simulations and direct experiments. Optical trapping of 1 and 2 μm beads shows that the Cooke-Triplet possesses an equally strong optical trap stiffness compared to the double Kepler lens design but reduces its lens system length by a factor of 2.6. Finally, we demonstrate how a Twyman-Green interferometer integrated in the Cooke-Triplet optical tweezers setup provides a fast and simple method to characterize the wavefront aberrations in the lens system and how it can help in aligning the optical components perfectly.