A process for the manufacture of an insulating product based on mineral fibres bonded by an organic binder, includes applying a sizing composition to the mineral fibres, forming an assembly of the mineral fibres, heating the assembly of mineral fibres until the sizing composition has cured, wherein the sizing composition includes the following constituents within the limits defined below, expressed as fractions by weight with respect to the total weight of the composition: from 80% to 98% of water, from 2% to 20% of water-soluble poly(furfuryl alcohol) and less than 0.5% of furfuryl alcohol, and the mineral fibres are fibres of aluminosilicate glass including aluminum oxide, Al2O3, in a fraction by weight of between 14% and 28%.