The starting point of this article is a conjecture of G. Valent [ISNM, Int. Ser. Numer. Math. 131, 227–237 (1999; Zbl 0935.30025)], concerning the order and type of an indeterminate Stieltjes moment problem related to birth and death processes. Concerning this conjecture, R. Romanov [Trans. Am. Math. Soc. 369, No. 2, 1061–1078 (2017; Zbl 1368.37072)] proved that if the processes have polynomial birth and death rates of degree \(p\geq 3\), the order is \(1/p\), as conjectured by Valent. In the paper under review, the authors prove that the type associated to the order must belong to a certain interval, explicitly exhibited. The techniques of the authors’ also lead to a new proof of Romanov’s theorem.