Non-Boltzmann sampling (NBS) methods are usually able to overcome ergodicity issues which conventional Monte Carlo methods often undergo. In short, NBS methods are meant to broaden the sampling range of some suitable order parameter (e.g., energy). For many years, a standard for their development has been the choice of sampling weights that yield uniform sampling of a predefined parameter range. However, Trebst et al. [Phys. Rev. E 70, 046701 (2004)] demonstrated that better results are obtained by choosing weights that reduce as much as possible the average number of steps needed to complete a roundtrip in that range. In the present work, we prove that the method they developed to minimize roundtrip times also equalizes downtrip and uptrip times. Then, we propose a discrete-parameter extension using such isochronal character as our main goal. To assess the features of the new method, we carry out simulations of a spin system and of lattice chains designed to exhibit folding transition, thus being suitable models for proteins. Our results show that the new method performs on a par with the original method when the latter is applicable. However, there are cases in which the method of Trebst et al. becomes inapplicable, depending on the chosen order parameter and on the employed Monte Carlo moves. With a practical example, we demonstrate that our method can naturally handle these cases, thus being more robust than the original one. Finally, we find an interesting correspondence between the kind of approach dealt with here and the committor analysis of reaction coordinates, which is another topic of rising interest in the field of molecular simulation. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3245304]13115