The drive toward more sensitive single-molecule manipulation techniques has led to the recent development of optical tweezers capable of resolving the motions of biological systems at the subnanometer level, approaching the fundamental limit set by Brownian fluctuations. One successful approach has been the dual-trap optical tweezers, in which the system of study is held at both ends by microspheres in two separate optical traps. We present here a theoretical description of the Brownian limit on the spatial resolution of such systems and verify these predictions by direct measurement in a Brownian noise-limited dual-trap optical tweezers. We find that by detecting the positions of both trapped microspheres, correlations in their motions can be exploited to maximize the resolving power of the instrument. Remarkably, we show that the spatial resolution of dual optical traps with dual-trap detection is always superior to that of more traditional, single-trap designs, despite the added Brownian noise of the second trapped microsphere.