There are binary systems (compounds) for which no structural solution can be found for a new high-pressure state by assuming a single phase. In accordance with Gibb's phase rule, an additional variable--composition--leads to an additional degree of freedom for a binary system (one more than in a one-component system). Although the bulk composition of a system may remain fixed, compositional variation between phases should be taken into account when considering phase transitions under pressure in binary compounds. This approach allows for a binary system the following kinds of phase transitions that are not possible in a one-component system: (i) phase (compound) decomposition into two phases with different compositions; (ii) phase synthesis from two initial phases; and (iii) phase separation from an initial phase into phases of different compositions. Examples of these kinds of high-pressure transformations and structure solution are given for the following binary systems: In-Bi, In-Sn, Hg-Sn, Cd-Sb and Sn-Bi.