Process for producing a polymer consisting of a linear main chain of beta-D-(1-3)- glucopyranosyl units having a single beta-D-glucopyranosyl unit (1-6) linked to a beta-D- glucopyranosyl unit of the linear main chain with an average branching degree of about 0.3, said process comprising the steps of: (i) culturing in a medium a genetically modified microorganism capable of producing a polymer consisting of a linear main chain of beta-D-(1-3)-glucopyranosyl units having a single beta-D-glucopyranosylunit (1-6) linked to a beta-D-glucopyranosyl unit of the linear main chain with an average branching degree of about 0.3, wherein the modification confers an increased activity -compared to a non-modified control microorganism of the same strain -of at least two gene products selected from the group consisting of (a) hexokinase, (b) phosphoglucomutase,. (c) UTP-glucose-1-phosphate uridyltrasferase, (d) 1,3–beta-glucan synthase (e) branching enzyme; under conditions allowing said microorganism to produce said polymer; (ii) optionally recovering said polymer from the medium.