Condensed Fukui function values of a number of closed-shell molecules have been calculated from Stockholder charges which were obtained using ab initio HF and DFT/B3LYP methods. The global softness parameters needed to evaluate local softness have been calculated using both Koopmans' approximation and the energy difference method. The calculated reactivity indices (condensed Fukui function and atomic softness) were used to predict the sites of electrophilic and nucleophilic attack in the molecules under investigation. In all cases, the atoms with the maximal value of condensed Fukui function and local softness are predicted to be the preferred sites of electrophilic or nucleophilic addition. The predictions thus made are in agreement with experiment and independent of the theoretical models used. The performance of the relative electrophilicity and relative nucleophilicity indices also was tested, but they were found not to have any special advantage as local reactivity descriptors.