We present an experimental study of the electrokinetic properties of a model colloidal system in which the number of ionizable sites per particle is controlled by exploiting the competitive adsorption between a ionic and a nonionic amphiphile. The adsorption of the nonionic amphiphile is monitored by light scattering. By measuring the electrophoretic mobility, we obtain the zeta-potential zeta of the particles. We find that zeta is independent from the ionic strength and strongly dependent on the surface density of ionizable sites, This indicates that in our system we can separately control zeta potential and ionic strength. In the investigated range of ionic strength and particle concentration, the Kerr constant of the dispersion is found to be proportional to the particle concentration, and does not contain any significant collective effect.