We propose to use the properties of the Lie algebra of the angular momentum to build symplectic integrators dedicated to the Hamiltonian of the free rigid body. By introducing a dependence of the coefficients of integrators on the moments of inertia of the integrated body, we can construct symplectic dedicated integrators with fewer stages than in the general case for a splitting in three parts of the Hamiltonian. We perform numerical tests to compare the developed dedicated fourth-order integrators to the existing reference integrators for the water molecule. We also estimate analytically the accuracy of these new integrators for the set of the rigid bodies and conclude that they are more accurate than the existing ones only for very asymmetric bodies.