In this paper we propose a new wider class of hypergeometric heavy tailed priors that are given as the convolution of a Student-t density for the location parameter and a Scaled Beta2 prior for the variance. These priors have heavier tails than Student-t prior, and the variances have a sensible behavior both at the origin and at the tail, making it suitable for objective analysis. Since the representation of our proposal is a scale mixture, it is suitable to detect sudden changes in the model. Finally we propose a Gibbs sampler using this new family of priors for modeling outliers and structural breaks in Bayesian dynamic linear models. It is clearly more suitable than the almost universal use of Inverted Gamma’s for the variances1) NIH 2) College of Natural Sciences, UPR