Light sheet fluorescence microscopy (LSFM) is rapidly becoming an essential technology for mesoscopic imaging of samples such as embryos and adult mouse organs. However, LSFM can suffer from optical artifacts for which there is no intrinsic solution. The attenuation of light due to absorbing material causes "shadow" artifacts along both the illumination and detection paths. Several approaches have been introduced to reduce this problem, including scanning illumination and multi-view imaging. However, neither of these approaches completely eliminates the problem. If the distribution of the absorbing material is complex, shadows cannot be avoided. We introduce a new approach that relies on multi-modal integration of two very different mesoscopic techniques. Unlike LSFM, optical projection tomography (OPT) can operate in transmission mode to create a voxel map of the 3D distribution of the sample's optical attenuation. Here, we demonstrate a hybrid instrument (OPTiSPIM) that can quantify this attenuation and use the information to correct the shadow artifacts of LSFM.