Scalar couplings between 13C spins can impair both resolution and sensitivity in 13C-labeled preparations. It is demonstrated that deconvolution of magic-angle-spinning NMR data with maximum entropy (MaxEnt) reconstruction allows the removal of splittings due to J-couplings without expenses in sensitivity. A combination of MaxEnt reconstruction in t2 with selective pulses in t1 produces fully J-resolved data in both dimensions. The possibility to obtain J-resolved 13C-13C data without compromising the sensitivity is particularly important for solid-state NMR of "difficult" biological samples, like membrane proteins, where sacrifices in signal-to-noise are fatal. The method is demonstrated using preparations of alpha-spectrin SH3 domain (62 residues) as small test system and of outermembrane protein G as example of a membrane protein with higher molecular weight (281 residues). Both preparations were obtained using [2-13C]-glycerol as the carbon source during the bacterial growth.