The conditions for the validity of the causal entropy bound ~CEB! are verified in the context of nonsingular cosmologies with classical sources. It is shown that they are the same conditions that were previously found to guarantee the validity of the CEB; the energy density of each dynamical component of the cosmic fluid needs to be sub-Planckian and not too negative, and its equation of state needs to be causal. In the examples we consider, the CEB is able to discriminate cosmologies which suffer from potential physical problems more reliably than the energy conditions appearing in singularity theorems.