We present radial velocities for 14 stars on the California & Carnegie Planet Search target list that reveal new companions. One star, HD 167665, was fit with a definitive Keplerian orbit leading to a minimum mass for the companion of 50.3 Mjup at a separation from its host of ~5.5 AU. Incomplete or limited phase coverage for the remaining 13 stars prevents us from assigning to them unique orbital parameters. Instead, we fit their radial velocities with Keplerian orbits across a grid of fixed values for Msini and period, P, and use the resulting reduced chi-square surface to place constraints on Msini, P, and semimajor axis, a. This technique allowed us to restrict Msini below the brown dwarf -- stellar mass boundary for an additional 4 companions (HD 150554, HD 8765, HD 72780, HD 74014). If the combined 5 companions are confirmed as brown dwarfs, these results would comprise the first major catch of such objects from our survey beyond ~3 AU. Comment: 29 pages, 14 figures, accepted to ApJ