The present invention is directed to a method for preparing a cellulose reactive adduct of polyvinylamide and a composition resulting from the method. The preparation of the cellulose reactive adduct is carried out close to a Critical Concentration defined herein. When the reaction is run close to this Critical Concentration, the risk of gelation is minimized, consumed glyoxal is maximized, and shelf live is enhanced. Additionally, the glyoxalated vinylamides of the present invention impart improved wet and dry strengthening efficiency to paper and paperboard when compared to adducts disclosed in previously described art.