A fundamental understanding of pure-component liquid-liquid phase separation in network-forming fluids remains an open challenge. While considerable progress has been recently made in demonstrating the existence of such a phase transition in some models via rigorous free energy calculations, it remains unclear what aspects of a model are sufficient, necessary, and/or prohibited in order for it to exhibit a liquid-liquid phase transition (LLPT). Among the simplest models capable of producing water-like anomalies is the sphericallysymmetrytwo-scale Jagla potential, for which an LLPT has been identified via equation of state calculations. In this work, we perform rigorous free energy calculations to demonstrate the existence of an LLPT in the Jagla model. We also utilize finite-size scaling analysis to calculate the surface tension associated with the LLPT.In addition to the thermodynamics of the model, we investigate the relaxation times for density and bondorientational order in both liquid phases and show that, contrary to assertions in the literature, the characteristic relaxation time of bond-orientational order is not orders of magnitude slower than that of density. To the contrary, we actually identify conditions for which density is the slowly relaxing order parameter. In addition to the original parameterization of the Jagla model, we provide in the “Appendix” preliminary free energy surface calculations for select parameterizations of the generalized family of Jagla potentials spanning from the original (anomalous,water-like) Jagla model to the Lennard-Jones model. These calculations indicate that, as the parameterization moves towards the Lennard-Jones limit, the LLPT disappears within the range of parametersexplored. Throughout the paper, we compare our results for the Jagla model with those found in the literature for the ST2 model of water in order to emphasize key similarities and differences between two models that exhibit pure-component liquid-liquid phase separation.