The short-wave (SW) direct radiative effect (DRE) during the summer 2019 heatwave produced partly by a moderate, long-lasting Saharan dust outbreak over Europe is analysed in this study. Two European sites (periods) are considered: Barcelona, Spain (23-30 June), and Leipzig, Germany (29 and 30 June), 1350 km apart from each other. Major data are obtained from AERONET and polarised Micro-Pulse Lidar (P-MPL) observations. Modelling is used to describe the different dust pathways, as observed at both sites. The coarse dust (Dc) and fine dust (Df) components (with total dust, DD = Dc + Df) are identified in the profiles of the total particle backscatter coefficient using the POLIPHON (POlarisation LIdar PHOtometer Networking) method in synergy with P-MPL measurements. This information is used to calculate the relative mass loading and the centre-of-mass height, as well as the contribution of each dust mode to the total dust DRE. Several aspects of the ageing of dust are put forward. The mean dust optical depth and its Df/DD ratios are, respectively, 0.153 and 24 % in Barcelona and 0.039 and 38 % in Leipzig; this Df increase in Leipzig is attributed to a longer dust transport path in comparison to Barcelona. The dust produced a cooling effect on the surface with a mean daily DRE of -9.1 and -2.5 W m.sup.-2, respectively, in Barcelona and Leipzig, but the Df/DD DRE ratio is larger for Leipzig (52 %) than for Barcelona (37 %). Cooling is also observed at the top of the atmosphere (TOA), although less intense than on the surface. However, the Df/DD DRE ratio at the TOA is even higher (45 % and 60 %, respectively, in Barcelona and Leipzig) than on the surface. Despite the predominance of Dc particles under dusty conditions, the SW radiative impact of Df particles can be comparable to, even higher than, that induced by the Dc ones. In particular, the Df/DD DRE ratio in Barcelona increases by +2.4 % d.sup.-1 (surface) and +2.9 % d.sup.-1 (TOA) during the dusty period. This study is completed by a second paper about the long-wave and net radiative effects. These results are especially relevant for the next ESA EarthCARE mission (planned in 2022) as it is devoted to aerosol-cloud-radiation interaction research.