We investigate a series of poly(amidoamine) starburst dendrimers (PAMAM) of different generations in acidic, aqueous solutions using small-angle neutron scattering (SANS). While the overall molecular size is found to be practically unaffected by a pD change, a strong generational dependence of counterion association is revealed. Upon increasing the dendrimer generation, the effective charge obtained from our SANS experiments only shows a small increase in contrast to the nearly exponential increase predicted by a recent atomic simulation. We also find that with the same degree of molecular protonation the specific counterion association, which is defined as the ratio of bound chloride anions to positively charged amines in solutions, is larger for higher-generation PAMAM dendrimer. The associated counterion density also increases upon increasing generation number.