The author introduces a stochastic order for point processes on \(\mathbb{R}_+\). The order depends on a so-called feasible valence function \(u\), and it can be adapted to various preferences that a decision maker may have by so-called \(u\)-concave functions. It is shown that the introduced order is weaker than the order \(\leq_{\text{st-}{\mathcal N}}\) of the reviewer and \textit{R. Szekli} [Adv. Appl. Probab. 27, No. 4, 1079-1103 (1995; Zbl 0849.60081)], and as such it may apply to specific situations for which the order \(\leq_{\text{st-}{\mathcal N}}\) is too general. Some instances in which the new order holds are listed. Finally, some applications are considered.