An extended version of the free-collision model was employed for the calculation of the electron detachment cross sections of several anions, with npi structures, i = 2, 3, 5 and 6, namely B−, Al−, C−, O−, S−, F− and Cl−, in collisions with noble gases in the intermediate-velocity regime. The calculations were performed only for the total electron detachment cross sections, except for the C− case, where partial electron-loss cross sections were obtained. Multiple electron loss was analysed within the independent particle model. The comparison of the calculated cross sections with the available experimental data shows good agreement in almost all cases.