The ongoing miniaturization of electronic circuits will eventually lead to signals consisting of only a few particles or molecules, but fluctuations will be a major interference in the operation of such circuits. Brownian circuits have been shown to exploit fluctuations by finding computational paths in circuits through a random search mechanism. This paper discusses Brownian circuits with decreased complexity, and shows designs of circuits with functionalities like counting, testing of conditional statements, memory, and arbitration of shared resources. We also discuss the potential of Brownian circuits for implementations by Single Electron Tunneling technology.