We compare the packing of meloxicam in all the meloxicam-containing crystal structures known up to now, with a special emphasis on meloxicam and its co-crystals with carboxylic acids, two of which, with adipic and terephthalic acids, have not been reported before. We argue that it is not the meloxicam dimers, as was claimed in Cheney et al., Cryst. Growth Des. 2010, 10, 4401-4413, but a fragment containing two molecules of meloxicam linked via a carboxylic acid molecule that is the primary structure-forming element in all the known 2:1 meloxicam:carboxylic acid co-crystals. Meloxicam molecules form H-bonded dimers in the crystals of meloxicam, but these dimers are no longer present in any of the known meloxicam co-crystals. The molecules of meloxicam in some of its co-crystal structures can be occasionally close to each other as a consequence of a certain steric relation defined by the size of the carboxylic acid molecules. However, these molecular pairs termed "dimers" by Cheney et al. are different from the dimers in the crystals of meloxicam and can be held together by weak H-bonds only (if any), therefore they can hardly be considered as a structure-forming unit. An improved dissolution of meloxicam co-crystals as compared to poorly soluble meloxicam is supposed to be related to the presence of meloxicam dimers linked by relatively strong H-bonds in the crystals of meloxicam and to the absence of these dimers in its co-crystals.