Brillouin fiber sensors have traditionally been limited to low-speed or static strain measurements due to the time-consuming frequency scans required. In the past decade, a number of novel high-speed measurement techniques have been proposed to enable Brillouin-based dynamic strain sensors. In this work, we present a new mechanism, which can limit the performance of high-speed dynamic Brillouin sensors. Specifically, we show that dynamic strain induced Doppler shifts can corrupt a distributed Brillouin strain measurement by introducing non-local signals throughout the fiber. We present a model showing that these non-local signals can introduce unacceptable levels of cross-talk or even exceed the local signal strength in reasonable operating conditions and experimentally observe these signals in a standard slope-assisted BOTDA sensor. Finally, we present a modified sensor architecture to address this issue and experimentally demonstrate low-noise (2.6 nε/Hz1/2), dynamic strain measurements with significantly reduced sensitivity to this type of non-local signal.