The amount of confidential information accessible through the Internet is growing continuously. In this scenario, the improvement of anonymizing methods becomes crucial to avoid revealing sensible information of individuals. Among several protection methods proposed, those based on the use of linear regressions are widely utilized. However, there is not a reason to assume that linear regression is better than using more complex polynomial regressions. In this paper, we present PoROP-k, a family of anonymizing methods able to protect a data set using polynomial regressions. We show that PoROP-k not only reduces the loss of information, but it also obtains a better level of protection compared to previous proposals based on linear regressions.