The crystal structures of N-methyl derivatives of the simplest amino acid glycine, namely sarcosine (C3H7NO2) and betaine (C5H11NO2), were studied upon cooling by single-crystal X-ray diffraction and single-crystal polarized Raman spectroscopy. The effects of decreasing temperature and increasing hydrostatic pressure on the crystal structures were compared. In particular, we have studied the behavior upon cooling of those structural motifs in the crystals, which are involved in structural rearrangement during pressure-induced phase transitions. In contrast to their high sensitivity to hydrostatic compression, the crystals of both sarcosine and betaine are stable to cooling down to 5 K. Similarly to most α-amino acids, the crystal structures of the two compounds are most rigid upon cooling in the direction of the main structural motif, namely head-to-tail chains (linked via the strongest N-H⋯O hydrogen bonds and dipole-dipole interactions in the case of sarcosine, or exclusively by dipole-dipole interactions in the case of betaine). The anisotropy of linear strain in betaine does not differ much upon cooling and on hydrostatic compression, whereas this is not the case for sarcosine. Although the interactions between certain structural motifs in sarcosine and betaine weaken as a result of phase transitions induced by pressure, the same interactions strengthen when volume reduction results from cooling.