In the second part of this paper, we consider the use of NUWS to decouple multiplets typically observed for uniformly C-labelled proteins due to the evolution of homonuclear 1 J CC scalar couplings during indirect chemical shift evolution periods. Such couplings give rise to signal modulations of the form cos n (πJt), where n is the number of coupled spins. Here we will focus on the case of terminal methyl groups, for which n = 1. Fortunately, aliphatic 1 J CC coupling constants are generally similar in magnitude, ranging between 32 and 40 Hz . Therefore, we employ a similar strategy to above, and seek to apply a constant noise NUWS scheme to remove the cos (πJt) modulation from the observed signal. However, a complication arises that was not present above: the zero crossings of cos (πJt) at 1/(2J), 3/(2J), etc. result in singularities in the required sampling schedule, n(t) = sec 2 (πJt) . The solution we propose here is to omit all measurements in the vicinity of these points, and subsequently use NUS reconstruction methods to fill in the gaps in the acquired FIDs (Fig. ). Although not randomly sampled, the low degree of sparsity nevertheless allows effective reconstructions to be obtained.