Logic programming with tabling and constraints (TCLP, tabled constraint logic programming) has been shown to be more expressive and in some cases more efficient than LP, CLP, or LP + tabling. Previous designs of TCLP systems did not fully use entailment to determine call/answer subsumption and did not provide a simple and well-documented interface to facilitate the integration of constraint solvers in existing tabling systems. We study the role of projection and entailment in the termination, soundness, and completeness of TCLP systems and present the design and an experimental evaluation of Mod TCLP, a framework that eases the integration of additional constraint solvers. Mod TCLP views constraint solvers as clients of the tabling system, which is generic w.r.t. the solver and only requires a clear interface from the latter. We validate our design by integrating four constraint solvers: a previously existing constraint solver for difference constraints, written in C; the standard versions of Holzbaur’s and , written in Prolog; and a new constraint solver for equations over finite lattices. We evaluate the performance of our framework in several benchmarks using the aforementioned solvers. Mod TCLP is developed in Ciao Prolog, a robust, mature, next-generation Prolog system.