The NMR resonances of C-13 spins in proximity to F-19 are often unusually broad, degrading resolution and limiting the ability to quantify the C-F interactions. We observe line-splittings and selective broadenings in a liquid crystal sample that strongly depend on the H-1 decoupling. We propose a simple rationalisation that successfully reproduces the experimental behaviour, and find that suitably adapted decoupling sequences effectively eliminate the line-broadenings. Experiments on solid samples show similar variations with decoupling sequence, and the same effects may be general to H-X-Y systems.