Light sheet fluorescence microscopy techniques have revolutionized biological microscopy enabling low-phototoxic long-term 3D imaging of living samples. Although there exist many light sheet microscopy (LSM) implementations relying on fluorescence, just a few works have paid attention to the laser elastic scattering source of contrast available in every light sheet microscope. Interestingly, elastic scattering can potentially disclose valuable information from the structure and composition of the sample at different spatial scales. However, when coherent scattered light is detected with a camera sensor, a speckled intensity is generated on top of the native imaged features, compromising their visibility. In this work, we propose a novel light sheet based optical setup which implements three strategies for dealing with speckles of elastic scattering images: (i) polarization filtering; (ii) reducing the temporal coherence of the excitation laser light; and, (iii) reducing the spatial coherence of the light sheet. Finally, we show how these strategies enable pristine light-sheet elastic-scattering imaging of structural features in challenging biological samples avoiding the deleterious effects of speckle, and without relying on, but complementing, fluorescent labelling.