The purpose of this paper is to make the standard promotion cure rate model (Yakovlev & Tsodikov, 1996) more flexible by assuming that the number of lesions or altered cells after some a treatment follows a fractional Poisson distribution (Laskin, 2003). It is proved that the well-known Mittag-Leffler relaxation function (Berberan-Santos, 2005) is a simple way to obtain a new cure rate model which is a compromise between the promotion and geometric cure rate models allowing for super-dispersion. So, the relaxed cure rate model developed here can be considered as a natural and less restrictive extension of the popular Poisson cure rate model at the cost of an additional parameter but a competitor to negative-binomial cure rate models (Rodrigues et al., 2009b). Some mathematical properties of a proper relaxed Poisson density, a simulation study and an illustration of the proposed cure rate model from the Bayesian point of view are presented. Key words: Bayesian inference, Poisson cure rate model, Fractional Poisson distribution, Mittag-Leffler relaxation function, Relaxed Poisson cure rate model, Geometric cure rate model.