We propose a new methodology for Thellier-type paleointensity experiments. In standard paleointensity experiments the blocking temperatures of most stable remanences are often not reached before thermal alteration of magnetic mineralogy begins, and subsequent data have to be discarded. We emphasize that when alteration begins at low temperature and continues throughout the experiment (which then fails in standard analyses), the resulting unblocking temperature (Tub) spectrum of the alteration product does not necessarily overlap with the whole Tub spectrum of natural remanent magnetization (NRM), because Tub depends on physical characteristics of the new grains, not the temperatures at which they were formed. NRM may survive in an uncontaminated higher Tub window. If alteration remanence only has low Tub then partial thermoremanent magnetization (pTRM) checks at temperature step Tj-1 can be used to correct for alteration that has occurred at Tj, and furthermore, thermal demagnetization of a full TRM acquired in the laboratory at the end of the progressive Thellier-Thellier experiment should reveal the true, uncontaminated Tub spectrum of the NRM in higher temperature intervals. We propose a new experimental sequence which allows monitoring and correction of alteration and provides two semi-independent estimates of palaeointensity in the circumstances described above. We illustrate the issues involved through new experimental work on igneous rocks from a Paleozoic charnockitic syenite, where we unravel TRM from multidomain isothermal remanence despite massive alteration during laboratory heating. Finally we point out the value of these experiments for verifying primary TRM in igneous rocks, indicating properties that distinguish TRM from other remanence. ¿ American Geophysical Union 1996