High-resolution, single-slice, high spatial and spectral resolution (HiSS) breast magnetic resonance imaging (MRI) provides improved lesion conspicuity, margin definition and internal definition, as compared to conventional clinical MRI - and thus may provide better lesion characterization and increase breast MRI specificity. Volumetric HiSS imaging is highly desirable, but was considered to be time-prohibitive. Specifically, the concern was that faster acquisition times -- necessitating a lower spectral resolution -- could compromise established advantages of HiSS imaging. In this pilot study, we demonstrate for the first time a fast, clinically practical, HiSS-based sequence that achieves full unilateral breast coverage, while preserving essential qualities of full-spectral resolution HiSS imaging. We imaged five patients of varying breast sizes at 1.5 T, with HiSS acquisitions performed after the standard clinical protocol, and lasting an average of 8.5 min. Maximum intensity projection (MIP) images of HiSS data were constructed and compared to MIPs of conventional clinical images. Single-slice images through three lesions were also compared. HiSS images achieved better fat suppression than the clinical fat-saturated sequence (fat signal SNR was reduced by 50% in HiSS images) as well as increased conspicuity, as assessed qualitatively by an experienced radiologist. Thus, we show that volumetric HiSS imaging can conserve the advantages of single-slice HiSS imaging and that further technical development of volumetric HiSS is desirable.