For operational purposes, in Enterprise Risk Management or in insurance for example, it may be important to estimate remote (but not extreme) quantiles of some function ƒ of some random vector. The call to ƒ may be time- and resource-consuming so that one aims at reducing as much as possible the number of calls to ƒ. In this paper, we propose some ways to address this problem of general interest. We then numerically analyze the performance of the method on insurance and Enterprise Risk Management real-world case studies.