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Following their success in numerous imaging and computer vision applications, deep-learning (DL) techniques have emerged as one of the most prominent strategies for accelerated MRI reconstruction. These methods have been shown to outperform conventional regularized methods based on compressed sensing (CS). However, in most comparisons, CS is implemented with two or three hand-tuned parameters, while DL methods enjoy a plethora of advanced data science tools. In this work, we revisit ${\ell }_1$-wavelet CS reconstruction using these modern tools. Using ideas such as algorithm unrolling and advanced optimization methods over large databases that DL algorithms utilize, along with conventional insights from wavelet representations and CS theory, we show that ${\ell }_1$-wavelet CS can be fine-tuned to a level close to DL reconstruction for accelerated MRI. The optimized ${\ell }_1$-wavelet CS method uses only 128 parameters compared to >500,000 for DL, employs a convex reconstruction at inference time, and performs within <1% of a DL approach that has been used in multiple studies in terms of quantitative quality metrics.