Compound hot and dry and dry-to-wet seesaw events are hydrometeorological extremes that involve the propagation of water deficits through the hydrological cycle, driven by multiple interactions between precipitation, temperature and soil moisture. Here we demonstrate new understanding of such events gained by directly modelling these interactions using copulas rather than treating each variable separately. New Zealand makes for a useful case study, owing to the occurrence of relatively high-magnitude extremes across strong hydroclimatic gradients. Standardised indices are constructed for soil moisture, temperature and precipitation using ERA5-Land for 1950–2021. A conventional bivariate copula model is used to capture the joint variation between precipitation and soil moisture indices for seesaw events, with a more novel trivariate (vine) copula for modelling all three indices during compound events. Differences in compound event detection are strongest in eastern regions, where evapotranspiration is more important for dry phase development. The copula approach reveals more frequent/extreme occurrence of compound events compared to coincident extremes in separate variables: for a 1-in-100-year vine copula event the equivalent magnitude coincident soil moisture and temperature extreme is a 141-year event (171-year for the coincident precipitation-temperature event). Large differences in seesaw event detection also occur in the east: compared to a 1-in-100-year bivariate copula event the equivalent soil moisture extreme is less frequent (126 years) but the precipitation extreme more frequent (65 years). These results highlight the advances that a copula approach can provide in terms of better understanding the magnitude-frequency characteristics of compound and seesaw events, as well as their drivers – critically important for managing the impacts of these events, especially in the context of climate change.