A method of fabricating a thermostructural composite material part includes making a fiber preform formed of yarns or tows and impregnated by a consolidating composition containing a carbon- or ceramic-precursor, transforming the carbon- or ceramic-precursor by pyrolysis, and then densifying the preform by chemical vapor infiltration. A consolidating composition is used that additionally contains refractory solid fillers in the powder form presenting mean grain size less than 200 nanometers and leaving, after pyrolysis, a consolidated solid phase in which the carbon or the ceramic derived from the precursor occupies a volume representing 3% to 10% of the apparent volume of the preform, and the solid fillers occupy a volume representing 0.5% to 5% of the apparent volume of the preform.