This paper tackles the issue of model consistency in identification procedures for SISO LTI compartmental systems of given order. In fact, in this case, the identified model must have a compartmental realization. In this paper, a finite set of constraints ensuring the existence of such a realization of a given order is proposed, in the case of real distinct eigenvalues. As a byproduct, the same set of conditions also ensure nonnegativity of the estimated impulse response.