H-MRSI is commonly performed with gradient phase encoding, due to its simplicity and minimal radio frequency (RF) heating (specific absorption rate). Its two well-known main problems-(i) "voxel bleed" due to the intrinsic point-spread function, and (ii) chemical shift displacement error (CSDE) when slice-selective RF pulses are used, which worsens with increasing volume of interest (VOI) size-have long become accepted as unavoidable. Both problems can be mitigated with Hadamard multislice RF encoding. This is demonstrated and quantified with numerical simulations, in a multislice phantom and in five healthy young adult volunteers at 3 T, targeting a 2-cm thick temporal lobe VOI through the bilateral hippocampus. This frequently targeted region (e.g. in epilepsy and Alzheimer's disease) is subject to strong, 1-2 ppm.cm regional B0, susceptibility gradients that can dramatically reduce the signal-to-noise ratio (SNR) and water suppression effectiveness. The chemical shift imaging (CSI) sequence used a 3-ms Shinnar-Le Roux (SLR) 90° RF pulse, acquiring eight steps in the slice direction. The Hadamard sequence acquired two overlapping slices using the same SLR 90° pulses, under twofold stronger gradients that proportionally halved the CSDE. Both sequences used 2D 20 × 20 rosette spectroscopic imaging (RSI) for in-plane spatial localization and both used RF and gradient performance characteristics that are easily met by all modern MRI instruments. The results show that Hadamard spectroscopic imaging (HSI) suffered dramatically less signal bleed within the VOI compared with CSI (<1% vs. approximately 26% in simulations; and 5%-8% vs. >50%) in a phantom specifically designed to test these effects. The voxels' SNR per unit volume per unit time was also 40% higher for HSI. In a group of five healthy volunteers, we show that HSI with in-plane 2D-RSI facilitates fast, 3D multivoxel encoding at submilliliter spatial resolution, over the bilateral human hippocampus, in under 10 min, with negligible CSDE, spectral and spatial contamination and more than 6% improved SNR per unit time per unit volume.