Extracranial lipid contaminants impede the reliable and accurate metabolite quantification with human brain MRSI. Elliptical localization with pulsed second order fields (ECLIPSE) was previously demonstrated for MRSI with inner volume selection (IVS), providing robust lipid suppression with improved elliptical brain coverage relative to a cubical ROI. In this work, alternative ECLIPSE-based OVS and IVS sequences were developed for human brain MRSI at 4T. Both ECLIPSE methods provide > 100-fold mean lipid suppression for short-TE MRSI. In addition, ECLIPSE-OVS consumes 30% of the power required by a traditional 8-slice OVS method, making ECLIPSE-OVS attractive for high field MRSI.