We work in the space of transitive, piecewise monotone maps of a fixed modality m with the topology of uniform convergence. There is an operator on this space which assigns to a map its constant slope model. This operator is discontinuous at points (maps) where perturbation can lead to a jump in entropy. Alseda and Misiurewicz conjectured that these are the only discontinuity points. We confirm the conjecture by a technique of "counting preimages". In particular, the operator is continuous if m≤4.