We discuss the evaluation of the real part of the elementary amplitudes in the context of a multiple diffraction model for pp elastic scattering earlier developed. The framework is based on the concepts of analyticity and polynomial boundedness, and the techniques of dispersion relations. Novel results concern the use of derivative dispersion relations at the elementary level (constituent-constituent interactions) and an optimization of these relations in terms of one free parameter. In addition to a theoretical improvement, we achieved a satisfactory description of the physical quantities. [S0556-2821(99)07009-5].5911