Palaeointensity estimates were made for a suite of five historical lava flows from Mt Askja, Iceland, with the purpose of testing the newly proposed domain-state corrections to the multispecimen parallel differential pTRM palaeointensity method (MSP), where pTRM stands for partial thermoremanent magnetization. Before beginning the experimental procedure, the chemical stability on heating to the determined pTRM induction temperature was assessed; some flows were found to be unaltered by heating, some displayed inconsistent repeatability, while one flow was severely affected by heating. To implement the domain-state corrections and interpret the data successfully, we had to implement two new approaches to the MSP method: (1) we used vector addition/subtraction in our calculations, and (2) we introduced a new selection/rejection criterion that improves the robustness of the estimates by preferentially removing outliers based on the error analyses of the linear regression. This rejection criterion typically rejected one or two points, and was found to significantly improve the estimates. With the exception of the one flow that displayed significant chemical alteration during the experiment, the palaeointensity estimates determined using the original MSP protocol yielded estimates within ±3 μT of the known field of 49.5 μT. The domain-state corrected MSP estimates were all within ±4 μT, with no clear relationship between the uncorrected and domain-state corrected palaeointensity estimates for this data set.