Future drought-hazard assessments using standardized indices depend on the period used to calibrate the probability distributions. This appears to be particularly important in a changing climate with significant trends in drought-related variables. This study explores the effect of using different approaches to project droughts, with a focus on changes in drought characteristics (frequency, duration, time spent in drought, and spatial extent), estimated with a calibration period covering recent past and future conditions (self-calibrated indices), and another one that only applies recent-past records (relative indices). The analysis focused on the Iberian Peninsula (IP), a hot-spot region where climate projections indicate significant changes by the end of this century. To do this, a EURO-CORDEX multi-model ensemble under RCP8.5 was used to calculate the Standardized Precipitation-Evapotranspiration Index (SPEI) at both 3- and 12-month timescales. The results suggest that projections of drought characteristics strongly depend on the period used to calibrate the SPEI, particularly at a 12-month timescale. Overall, differences were larger for the near future when relative indices indicated more severe droughts. For the distant future, changes were more similar, although self-calibrated indices revealed more frequent and longer-lasting droughts and the relative ones a drought worsening associated with extremely prolonged drought events.