Optical traps or "optical tweezers" have become an indispensable tool in understanding fundamental biological processes. The environment, the instrument components, and the overall design all have important roles in determining the spatial resolution of an optical trap. However, even with careful attention to these details, the spatial resolution of the optical tweezers is still fundamentally limited by the forces that induce Brownian fluctuations of the trapped microspheres. In this article, we focus on the ways in which the design and implementation of an experiment - the choice of bead size, tether length, and even the method in which the motions of the beads are monitored - can have a large impact on the fundamental resolution of the measurement. By investigating how the Brownian fluctuations depend on experimental parameters and the detection method, we develop a set of guidelines for designing a high-resolution experiment, with a prescription for minimizing the effect of Brownian fluctuations, thus maximizing the resolution of the experiment.