Changes in rank-dependent income-related health inequality measures over time may usefully be decomposed into contributions due to changes in health outcomes and changes in individuals' positions in the income distribution. This paper establishes the normative implications of this type of decomposition by embedding it within a broader analysis of changes in the ‘health achievement’ index. We further show that the choice of health inequality measure implies a particular vertical equity judgement, which may be expressed on a common scale in terms of the concentration index of health changes that would be inequality preserving. We illustrate the empirical implications of this choice by reporting results from a longitudinal analysis of changes in income-related health inequality in Great Britain using the concentration, the Erreygers and Wagstaff indices of health attainments and the concentration index of health shortfalls. Copyright © 2012 John Wiley & Sons, Ltd.