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BACKGROUND AND PURPOSE: Clinical adoption of 7T MRI has been limited by lengthy acquisitions. Acceleration techniques, such as controlled aliasing in parallel imaging (CAIPI) and compressed sensing (CS), can reduce scan time but are prone to artifacts and noise. This work combines CAIPI and CS within a unified, two-step deep-learning (DL) reconstruction framework to leverage their strengths: CAIPI for controlled aliasing with improved conditioning, CS for additional incoherent undersampling, and DL to reduce residual aliasing and CS-related artifacts. This hybrid approach aims to maintain image quality while enabling higher net acceleration and reducing scan time. MATERIALS AND METHODS: In this paired within-subject study, 30 patients underwent 7T sampling perfection with application-optimized contrasts using different flip angle evolutions (SPACE) FLAIR and 30 patients underwent 7T SPACE T2 acquisitions. Each scan included a reference CAIPI-DL protocol (acceleration factor=6; ∼7 minutes) and a CS-CAIPI-DL protocol (acceleration factor=14; ∼3.5 minutes). Image quality was assessed quantitatively using structural similarity index, peak signal-to-noise ratio, gradient-domain mean squared error, contrast-to-noise ratio, noise, ghosting ratio, and Natural Image Quality Evaluator (NIQE), as well as blinded qualitative assessments. Statistical comparison used linear mixed-effects models with false discovery rate correction. RESULTS: CS-CAIPI-DL reduced scan time by approximately 50% without significant differences in contrast-to-noise ratio or noise for either sequence. Ghosting ratios were significantly lower with CS-CAIPI-DL for both FLAIR (∼10% reduction; q