Compressed sensing (CS) is widely used to accelerate clinical diffusion MRI acquisitions, but it is not widely used in preclinical settings yet. In this study, we optimized and compared several CS reconstruction methods for diffusion imaging. Different undersampling patterns and two reconstruction approaches were evaluated: conventional CS, based on Berkeley Advanced Reconstruction Toolbox (BART-CS) toolbox, and a new kernel low-rank (KLR)-CS, based on kernel principal component analysis and low-resolution-phase (LRP) maps. 3D CS acquisitions were performed at 9.4T using a 4-element cryocoil on mice (wild type and aMAP6knockout). Comparison metrics were error and structural similarity index measure (SSIM) on fractional anisotropy (FA) and mean diffusivity (MD), as well as reconstructions of the anterior commissure and fornix. Acceleration factors (AF) up to 6 were considered. In the case of retrospective undersampling, the proposed KLR-CS outperformed BART-CS up to AF = 6 for FA and MD maps and tractography. For instance, for AF = 4, the maximum errors were, respectively, 8.0% for BART-CS and 4.9% for KLR-CS, considering both FA and MD in the corpus callosum. Regarding undersampled acquisitions, these maximum errors became, respectively, 10.5% for BART-CS and 7.0% for KLR-CS. This difference between simulations and acquisitions arose mainly from repetition noise, but also from differences in resonance frequency drift, signal-to-noise ratio, and in reconstruction noise. Despite this increased error, fully sampled and AF = 2 yielded comparable results for FA, MD and tractography, and AF = 4 showed minor faults. Altogether, KLR-CS based on LRP maps seems a robust approach to accelerate preclinical diffusion MRI and thereby limit the effect of the frequency drift.