Financial protection is a health system goal for all countries. Assessing progress on this relies on measuring the incidence of catastrophic health expenditures (proportion of the population whose out-of-pocket (OOP) payments for health surpass a certain threshold of household resources). Standard approaches rely on selective thresholds, however this masks varying intensities of financial hardship and poses a measurement challenge as incidence is sensitive to the choice of the threshold. We address this problem by applying the dominance approach, which tests differences in catastrophic incidence curves over a continuous range of thresholds. Iran is an interesting country for empirical application of the dominance approach given its historically high reliance on OOP payments to finance its health system and its commitment to improving financial protection through several national health policies over the last two decades. Using data from annual Household Income and Expenditure Surveys from 2005 to 2017 (sample size: 26,851-39,088 households), incidence was analyzed following this novel approach. Distribution of incidence across socio-economic status was also analyzed by estimating concentration indices and across health services or products by estimating average shares of each item. Results showed that over time catastrophic health expenditures increased for thresholds lower than 25% and decreased for thresholds higher than 35%. Catastrophic health expenditures were more equally distributed across income levels at lower thresholds, becoming concentrated amongst the rich as the threshold rose. Medicines represented the largest share of catastrophic spending for the poorest; medicines, dentistry, inpatient and ancillary services for the richest. This is the first study to apply dominance methods to analyze catastrophic health expenditures in a country over time. The analysis provides a nuanced picture of who incurs catastrophic health expenditures, to what extent hardship is experienced and what were the drivers of these expenditures - thus providing a better basis for policy responses.