Abstract: A process for treating a container having a normally solid, polymer surface with a sulfur-containing compound is carried out in two stages. In the first stage, a first sulfonation treatment is conducted by: (i) contacting the surface at a temperature of about 115.degree. to about 140.degree. F. with a first sulfur-containing compound; and, (ii) washing the surface with an aqueous liquid. Optionally, in the first stage, after the surface is contacted with the first sulfur-containing compound, but before it is washed with the aqueous liquid, the surface may be contacted with a first neutralizing agent. In the second stage, a second sulfonation treatment is conducted by contacting the surface with a second sulfur-containing compound, a second neutralizing agent and washing the surface with an aqueous liquid. The second sulfur-containing compound and the second neutralizing agent may be the same as or different than the first sulfur-containing compound and the optional first neutralizing agent, respectively.