The intensification of compound hot-dry events due to climate change is a pressing concern, underscoring the need for precise analysis. However, the impact of different dry indicators on projections of these events has not been quantitatively evaluated, nor has its importance been compared with other sources of uncertainty. Here we examine the sensitivity of projected changes in compound hot-dry events to different dry indicators. We use data from 22 Coupled Model Intercomparison Project Phase 6 (CMIP6) models to characterize global dry conditions based on precipitation, runoff, soil moisture, and a multivariate index combining these variables through trivariate copulas. Our findings reveal large differences in projected changes in the likelihood of compound hot-dry events across different dry indicators. While model uncertainty remains the primary source of uncertainty for compound hot-dry event projections, the uncertainty associated with dry indicators is also substantial, surpassing scenario uncertainty in specific regions.