The link between the growth of supermassive black holes and their host galaxies is still poorly understood. Clues to this may come from observations of the most obscured galaxy nuclei, which are thought to be the sites of the most vigorous black hole growth. We have just completed a paper, “Hidden or missing outflows in highly obscured galaxy nuclei?” (Falstad+), which addresses one aspect of this broad science question. In the paper we compare the intensity of these obscured nuclei (diagnosed by the emission from vibrationally excited HCN molecules) with the speed of molecular outflows (traced by the OH molecule). We found that the most apparently extreme nuclei lack fast outflows and the comparatively weaker nuclei show the fastest outflows. This could signify an evolutionary sequence where some form of energy injection clears gas from the centers of galaxies, thus reducing the intensity of these embedded nuclear cores. Alternately, this finding could be due to projection and optical depth effects. Both possibilities are discussed in the paper. We have posted a preprint and the paper will appear in Astronomy and Astrophysics.