Differential privacy is well-known because of the strong privacy guarantees it offers: the results of a data analysis must be indistinguishable between data sets that differ in one record. However, the use of differential privacy may limit the accuracy of the results significantly. Essentially, we are limited to data analyses with small global sensitivity (although some workarounds have been proposed that improve the accuracy of the results when the local sensitivity is small). We introduce individual differential privacy (iDP), a relaxation of differential privacy that: (i) preserves the strong privacy guarantees that differential privacy gives to individuals, and (ii) improves the accuracy of the results significantly. The improvement in the accuracy comes from the fact that the trusted party does a more precise assessment of the risk associated to a given data analysis. This is possible because we allow the trusted party to take advantage of all the available information, namely the actual data set.