We discuss the effect that is produced on the binary logit model with one explanatory factor, when the researcher decides to join some levels of the factor. Based on the reference parametrization and the saturated model a procedure is suggested, that takes advantage of the calculations of the first adjustment and corrects the distribucional supposition around the variance. As a result, it produces estimations more efficiently and with more precision, than those which take place if it is decided to repeat the usual logit fit. Once placed the topic in perspective, we develop the equations that support the suggested procedure, based on asymptotic theory. We illustrate with an example the difference between the suggested procedure and the usual one. By developing an extensive simulation, some solid trends appear in favour of the first one, especially when the probabilities of success of the response (Y = 1), associated with the categories of the explanatory factor included in the group, are less similar each other.