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Purpose: The expanded encoding model incorporates spatially- and time-varying field perturbations for correction during reconstruction. So far, these reconstructions have used the conjugate gradient method with early stopping used as implicit regularization. However, this approach is likely suboptimal for low-SNR cases like diffusion or high-resolution MRI. Here, we investigate the extent that l1-wavelet regularization, or equivalently compressed sensing (CS), combined with expanded encoding improves trade-offs between spatial resolution, readout time and SNR for single-shot spiral diffusion-weighted imaging at 7T. The reconstructions were performed using our open-source GPU-enabled reconstruction toolbox, MatMRI, that allows inclusion of the different components of the expanded encoding model, with or without CS. Methods: In vivo accelerated single-shot spirals were acquired with five acceleration factors (2-6) and three in-plane spatial resolutions (1.5, 1.3, and 1.1 mm). From the in vivo reconstructions, we estimated diffusion tensors and computed fractional anisotropy maps. Then, simulations were used to quantitatively investigate and validate the impact of CS-based regularization on image quality when compared to a known ground truth. Results: In vivo reconstructions revealed improved image quality with retainment of small features when CS was used. Simulations showed that the joint use of the expanded encoding model and CS improves accuracy of image reconstructions (reduced mean-squared error) over the range of acceleration factors investigated. Conclusion: The expanded encoding model and CS regularization are complementary tools for single-shot spiral diffusion MRI, which enables both higher spatial resolutions and higher acceleration factors.