This research addresses how survival analysis can be improved when dealing with subjects who may never experience the event of interest. This paper proposes a two-step procedure to improve upon the maximum likelihood estimator in mixture cure models, especially when sample sizes are limited. Such models are commonly used when estimating data with the iterative EM algorithm. The method uses presmoothing by creating a nonparametric estimator and then projecting it on a parametric class. By doing so, it can improve upon traditional maximum likelihood estimation techniques that can be less accurate with small sample sizes. This approach is especially relevant in survival analysis contexts where the presence of cured subjects can skew results. An extensive simulation study for the logistic-Cox model demonstrates that the proposed method outperforms existing approaches. The paper's practical value is further illustrated through applications to two melanoma datasets. This two-step approach could lead to more reliable and accurate predictions in survival analysis, particularly when dealing with small or complex datasets.