This is a clever idea to use spin locking to essentially desensitize desired coherences from unwanted gradient spillover effects from a gradient set adjacent to the one which is being actively used. I have only a few minor suggestions to the manuscript. 

1. Reference to parallel imaging in the introduction is not really appropriate. For example SENSE (Pruessman) uses measured coil sensitivity maps to reconstruct undersampled data from a single sample and multiple detectors, so this is a very different scenario from the one here. 

2. The authors often talk about spillover from one detector to another, by which they mean one coil/gradient combination to another, but i think this would be better phrased as gradient spillover, or the effects of gradient spillover, to separate from RF spillover. 

3. How generalizable is this approach to a much more complicated spin system, ie not just an IS heteronuclear one. Presumably spin locking would only be applicable to certain coherences at certain evolution times, or is this not correct. It would be good to see some discussion of this topic at the end of the paper. 

4. The authors state the pulse optimization does not account for homonuclear (HH or XX) coupling. Is this theoretically possible assuming a certain coupling constant, or does the problem become intractable for realistic spin systems?

5. The final paragraph of the conclusion is very strangely worded and could easily be removed. 

Really nice work to mitigate gradient field spillover in parallel NMR spectroscopy, a technique aimed at increasing throughput for applications like drug discovery. The authors introduce "coherence-locking" (CLOC) pulses, designed via optimal control theory, to protect spin coherences from dephasing caused by gradient pulses in adjacent detectors. The study tests this compensation scheme in pulsed gradient spin echo (PGSE) and heteronuclear single quantum coherence (HSQC) experiments, using a custom parallel NMR probe. A great idea and well executed. Although there are some limitations (related to spin-system specificity), the approach is innovative and potentially useful and therefore fully worthy of publication. The authors may wish to add a statement explaining the generalizability of approach)