A model-potential method is employed to calculate binding, elastic scattering, and annihilation of positrons for a number of atoms and small nonpolar molecules, namely, Be, Mg, He, Ar, H 2 , N 2 , Cl 2 , and CH 4 . The model potential contains one free parameter for each type of atom within the target. Its values are chosen to reproduce existing ab initio positron-atom binding energies or scattering phase shifts. The calculations are performed using a Gaussian basis for the positron states, and we show how to obtain values of the scattering phase shifts and normalized annihilation rate Z eff from discrete positive-energy pseudostates. Good agreement between the present results and existing calculations and experimental data, where available, is obtained, including the Z eff value for CH 4 , which is strongly enhanced by a low-lying virtual positron state. An exception is the roomtemperature value of Z eff for Cl 2 , for which the present value is much smaller than the experimental value obtained over 50 years ago. Our calculations predict that among the molecular targets studied, only Cl 2 might support a bound state for the positron, with a binding energy of a few meV.