Some novel cancer treatments can induce long sustained response leading to prolonged survival, potentially indicating a cure. Projection of overall survival (OS) with these treatments using standard parametric methods – often performed with very early cuts of the trial data – can produce a more rapid projected rate of death than expected. Cure mixture models have been proposed to better capture the full benefit of treatment. These models explicitly account for the possibility of some patients achieving a cure, and estimates the proportion cured that yields the mixture of cancer and non-cancer deaths providing best fit to the data. We use an example based on published survival with over ten years follow-up with immunotherapy for melanoma to illustrate the risks of premature application of cure models. The data show a clear flattening of the OS curve at around 20%, suggesting that the risk of cancer-related deaths has become negligible. We applied cure models and standard parametric fitting analyses on multiple simulated interim cuts of the data at yearly intervals. We found that while the cure model provided best fit to the observed curve, the estimated cure fraction and long term projected OS greatly exaggerated the effect of treatment. The estimated proportion cured aligned with the final observed plateau when the deceleration of mortality was manifested in the data. This highlights the risks of misleading projections with models that otherwise meet the usual evaluation criteria (e.g., fit statistics, close prediction of the data). The shape of the extrapolation and the plausibility of the estimated cure fraction are critical with these methods. With a strong prior belief of the existence of a potential cure, it is tempting to resort to cure models for early projection analyses; our findings suggest a more conservative approach is advisable.