In this paper, a modified Weibull model is proposed to fit microbial survival curves. This model can incorporate shoulder and/or tailing phenomena if they are encountered. We aim to obtain an accurate fit of the "primary" modelling of the bacterial inactivation and to provide a useful and meaningful model for biologists and food industry. A delta parameter close to the classical concept of the D value, established for sterilisation processes, is used in the model. The specific parameterisation of the Weibull model is evaluated for the parameter of interest delta. The goodness-of-fit of the model is compared to the one produced by the model proposed by Geeraerd et al., [Geeraerd, A.H., Herremans, C.H., Van Impe, J.F., 2000. Structural model requirements to describe microbial inactivation during a mild heat treatment. Int. J. Food Microbiol. 59, 185-209.] on experimental data. As our model provides good fits for the different types of survival curves analysed, further research can focus on the development of suitable secondary model types. In this respect, it is interesting to note that the delta parameter is close to the D concept.