A method for producing insoluble alpha-1,3-glucan is disclosed. Embodiments of the method comprise providing (i) oligosaccharides that comprise alpha-1,3 and alpha-1,6 glycosidic linkages, or (ii) oligosaccharides derived from a glucosyltransferase reaction; and contacting at least water, sucrose, a glucosyltransferase enzyme, and the oligosaccharides provided in the first step. Glucosyltransferase reaction compositions embodying such a method, and insoluble products thereof, are also disclosed. Yield and other product benefits can be realized when practicing the disclosed subject matter.