Combustion and other high-temperature processes frequently result in the emission of aerosols in the form of polydisperse fractal-like aggregates made of condensed-phase nanoparticles (soot for instance). If certain conditions are met, the emitted aerosol particles are known to evolve into important cloud condensation nuclei (CCN) in the atmosphere. In this work, the hygroscopic parameter κ of complex morphology aggregates is calculated from the supersaturation-dependent activated fraction Fa=Fa(SS) in the frame of κ-Köhler theory. The particle size distribution is approximated with the morphology-corrected volume equivalent diameter calculated from the electrical mobility diameter by taking into account the diameter of the primary particle and the fractal dimension of the aggregate experimentally obtained from transmission electron microscopy measurements. Activation experiments are performed in water supersaturation conditions using a commercial CCN-100 condensation nuclei counter. The model is tested in close-to-ideal conditions of size-selected, isolated spherical particles (ammonium sulfate nanoparticles dispersed in nitrogen), then with complex polydisperse fractal-like aggregates (soot particles activated by exposure to ozone with κ as low as 5×10−5) that represent realistic anthropogenic emissions in the atmosphere.