In this paper we introduce a family of languages called Deterministic λ-free Petri net languages (DPNLs). We show that the controllability of a DPNL K is contained in Σ* with respect to a DPNL L is contained in Σ* is decidable. That is, it is possible to decide if (i) K is contained in L, and (ii) the intersection of sets KΣu and L is contained in K, where Σc = where the union of sets where the union of sets σu and Σc and the intersection of sets Σu and Σc = 0. We also show that this family of languages strictly includes the family of Free-labeled Petri net languages (FLPNLs), another family of languages where the controllability of one language with respect to another is decidable. Essentially this paper is an extension of reference.