The International Commission on Radiological Protection (ICRP) reference male and female adult phantoms, described in Publication 110, are voxel phantoms based on whole-body computed tomography scans of a male and a female patient, respectively. The voxel in-plane resolution and the slice thickness, of the order of a few millimetres, are insufficient for proper segmentation of smaller tissues such as the lens of the eye, the skin, and the walls of some organs. The calculated doses for these tissues therefore present some limitations, particularly for weakly penetrating radiation. Similarly, the Publication 110 phantoms cannot represent 8-40-µm-thick target regions in respiratory or alimentary tract organs. Separate stylised models have been used to represent these tissues for calculation of the ICRP reference dose coefficients (DCs). ICRP Committee 2 recently initiated a research project, the ultimate goal of which is to convert the Publication 110 phantoms to a high-quality polygon-mesh (PM) format, including all source and target regions, even those of the 8-40-µm-thick alimentary and respiratory tract organs. It is expected that the converted phantoms would lead to the same or very similar DCs as the Publication 110 reference phantoms for penetrating radiation and, at the same time, provide more accurate DCs for weakly penetrating radiation and small tissues. Additionally, the reference phantoms in the PM format would be easily deformable and, as such, could serve as a starting point to create phantoms of various postures for use, for example, in accidental dose calculations. This paper will discuss the current progress of the phantom conversion project and its significance for ICRP DC calculations.