The silicone composition is one that contains liquid silicone, at least one insoluble functionalizing filler, such as a thermally or electrically conductive filler, and a non-liquid anti-thickening or non-thickening anti-settling material, such as a cellulose compound or polysaccharide. In a system that contains liquid silicone and insoluble functionalizing filler(s), a polysaccharide functions as an anti-thickening or non-thickening anti-settling material, providing a low-viscosity and filler-rich silicone composition.