The Kadomtsev-Petviashvili and Boussinesq equations (u xxx − 6uu x ) x − u tx ± u yy = 0, (u xxx − 6uu x ) x + u xx ± u tt = 0, are completely integrable, and in particular, they possess the three-soliton solution. This article aims to expose a uniqueness property of the Kadomtsev-Petviashvili (KP) and Boussinesq equations in the integrability theory. It is shown that the Kadomtsev-Petviashvili and Boussinesq equations and their dimensional reductions are the only integrable equations among a class of generalized Kadomtsev-Petviashvili and Boussinesq equations (uwhere the a i j 's are arbitrary constants and M is an arbitrary natural number, if the existence of the three-soliton solution is required.