Employing optical fiber to deliver the trapping laser to the sample chamber significantly reduces the size and costs of optical tweezers (OT). The utilization of fiber decouples the OT from the microscope, providing scope for system portability, and the potential for uncomplicated integration with other advanced microscopy systems. For use with an atomic force microscope, the fiber must be inserted at an angle of 10 deg to the plane of the sample chamber floor. However, the literature states that optical trapping with a single fiber inserted at an angle ≤20 deg is not possible. This paper investigates this limitation and proposes a hypothesis that explains it. Based on this explanation, a tapered-fiber optical tweezer system is developed. This system demonstrates that such traps can indeed be made to function in three-dimensions (3-D) at insertion angles of ≤10 deg using relatively low optical powers, provided the fiber taper is optimized. Three such optimized tapered fiber tips are presented, and their ability to optically trap both organic and inanimate material in 3-D is demonstrated. The near-horizontal insertion angle introduced a maximum trapping range (MTR). The MTR of the three tips is determined empirically, evaluated against simulated data, and found to be tunable through taper optimization.