We investigate a class of models for viscoelastic fluids, in which the elastic stress is determined by a conformation tensor, and the conformation tensor is linked to the velocity field by a system of ordinary differential equations. We study the question which values of the conformation tensor can be reached in a homogeneous flow, subject to a given initial condition and arbitrary velocity fields. This problem is a special "easy" case for the question of controllability of viscoelastic flows. For a class of models, we show that constraints on the values of the conformation tensor are given by lower and/or upper bounds on its determinant. The behavior of seemingly similar models, e.g. the PTT, Giesekus and Peterlin dumbbell models, turns out to be surprisingly different. (c) 2008 Elsevier B.V. All rights reserved.