The power available from narrow-linewidth single-transverse-mode fiber amplifiers is primarily limited by the onset of stimulated Brillouin scattering. One approach for increasing the SBS threshold that has shown recent promise is to tailor the acoustic velocity within the fiber cross-section to suppress Brillouin gain. Relating the SBS threshold to an acousto-optic effective area has yielded a theory which contradicts experimental measurements that indicate the nonlinear optical effective area of the tested SBS suppressing and Higher Order Mode (HOM) fibers is of primary importance in the nonlinear process. In this work, we present a new formalism for determining the Brillouin gain in fibers with inhomogeneous acoustic velocity which may be implemented with a wide variety of computational methods. We find that the Brillouin gain amplitude and spectrum are independent of the acousto-optic effective area and that they reduce to the bulk result for conventional step-index fibers. Implementing a finite-element method, we find that an SBS-suppressing design employing a negative focal length acoustic lens exhibits a broadened gain spectrum and reduced gain amplitude relative to step-index fibers. The SBS threshold of this fiber is increased by 8.4 dB relative to a standard large mode area fiber, each with an identical 6 meter length. Designs that further flatten the Brillouin gain spectrum have the potential to further increase the SBS threshold leading to higher single-frequency output power from devices incorporating these fibers.© (2009) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.