A method is presented for making alkoxy-modified silsesquioxanes (AMS) or co-alkoxy-modified silsesquioxanes (co-AMS,) comprising the steps of (a) combining as a reaction mixture (i) water, (ii) an acid-stable solvent for the water, (iii) a solid strong cationic hydrolysis and condensation catalyst, and (iv) a trialkoxysilane compound, (b) allowing the reaction mixture to react for about 0.5 hours to about 200 hours to form the alkoxy-modified silsesquioxanes; and (c) recovering the alkoxy-modified silsesquioxanes from the reaction mixture. The use of solid strong cationic catalysts in this reaction system is advantageous because they remain as solids throughout the reaction, allowing simplified separation of the solid catalyst from the soluble AMS or co-AMS products, resulting in total or near total recovery of the AMS or co-AMS products, the products being free of, or substantially free of residual acid catalyst, as well as virtual total recovery of the catalyst for recycling. The improved AMS and co-AMS compounds, vulcanizable rubber compounds containing them, and a pneumatic tire having a component made from the vulcanized rubber compounds are also presented.