Optical fiber sensors utilizing Brillouin scattering rely on the principle that the Brillouin frequency shift is a function of the local temperature or strain. Conventional optical fibers, such as standard telecommunications single-mode fibers, have been successfully used in these applications, and most typically in the time domain, such as with BOTDR. Such conventional fibers however are susceptible simultaneously to both temperature and strain, requiring either at least two fibers or specialized cabling to distinguish the effects of a local stress from those of a local change in temperature. Recently, methods utilizing fibers possessing at least two Brillouin frequency shifts, each with different temperature or strain coefficients have been proposed. However, realizing such fibers is challenging, requiring fibers with regions of very different compositions, all of which must have substantial overlap with the optical field, posing significant manufacturing challenges. We present several new specialty optical fibers based on novel and unconventional fabrication techniques with significant potential for use in distributed fiber sensor systems. First, we describe a class of fibers fabricated from materials whose Brillouin frequency shifts are immune to either temperature or strain, with a demonstration of the former using fiber derived from sapphire crystal, and modeling and measurements predicting the latter. The 'Brillouin-athermal' fiber enables the measurement of a local strain, independent of the local temperature. Second, we describe and demonstrate a novel group of longitudinallygraded (chirped) fibers enabling easily-implemented frequency-domain systems; affording the potential to simplify and reduce the cost of Brillouin-based distributed sensors.