In vivo, high-field MR spectroscopic imaging (MRSI) profits from signal-to-noise ratio (SNR) gain and increased spectral resolution. However, bandwidth limitations of slice-selective excitation and refocusing pulses lead to strong chemical-shift displacement at high field strength when using conventional MRSI localization based on PRESS. Consequential metabolic information, particularly of border regions such as cortical brain tissue, is distorted. In addition, lipid contamination remains a major confound. To address these problems it is proposed to abandon PRESS selection and rely on a novel scheme of highly selective T(1)- and B(1)-insensitive outer-volume suppression in combination with slice-selective spin-echo acquisition for brain MRSI. Multiple cycles of overlapping suppression slabs are applied with flip angles optimized to account for tissue-dependent T(1) relaxation times and band crossings. Broadband frequency modulated saturation pulses with polynomial phase-response are utilized in order to minimize chemical-shift displacement. Efficacy of the outer-volume suppression sequence was simulated and evaluated in vitro and in vivo. Brain MRSI localization at 3T was significantly improved and reliable suppression of short-range lipid contamination enabled, leading to substantial enhancement of spectral quality, particularly in cortical tissue. Hence, the new method holds potential to expand the applicability of high-field MRSI to the entire brain.