We report the effect of pressure on the crystal structures of betaine monohydrate (BTM), L-cysteic acid monohydrate (CAM) and S-4-sulfo-L-phenylalanine monohydrate (SPM). All three structures are composed of layers of zwitterionic molecules separated by layers of water molecules. In BTM the water molecules make donor interactions with the same layer of betaine molecules, and the structure remains in a compressed form of its ambient-pressure phase up to 7.8 GPa. CAM contains bi-layers of L-cysteic acid molecules separated by water molecules which form donor interactions to the bi-layers above and below. This phase is stable up to 6.8 GPa. SPM also contains layers of zwitterionic molecules with the waters acting as hydrogen-bond donors to the layers above and below. SPM undergoes a single-crystal to single-crystal phase transition above 1 GPa in which half the water molecules reorient so as to form one donor interaction with another water molecule within the same layer. In addition, half of the S-4-sulfo-L-phenylalanine molecules change their conformation. The high-pressure phase is stable up to 6.9 GPa, although modest rearrangements in hydrogen bonding and molecular conformation occur at 6.4 GPa. The three hydrates had been selected on the basis of their topological similarity (CAM and SPM) or dissimilarity (BTM) with serine hydrate, which undergoes a phase transition at 5 GPa in which the water molecules change orientation. The phase transition in SPM shows some common features with that in serine hydrate. The principal directions of compression in all three structures were found to correlate with directions of hydrogen bonds and distributions of interstitial voids.