Secondary ion mass spectrometry (SIMS) is the oldest and most sensitive analytical technique for in situ U–Pb geochronology. This paper introduces a new algorithm for SIMS data reduction that treats data as compositional data, which means that the relative abundances of ²⁰⁴Pb, ²⁰⁶Pb, ²⁰⁷Pb, and ²³⁸Pb are processed within a tetrahedral data space or simplex. The new method is implemented in an eponymous computer programme that is compatible with the two dominant types of SIMS instruments.