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Copper single crystals have been simultaneously strengthened by solved gold-atoms and by incoherent SiO₂-particles. The critical resolved shear stress (CRSS) τs of a binary copper–gold solid solution and the CRSS τt of the same solid solution additionally strengthened by SiO₂-particles have been measured in the temperature range 90–283 K. From the experimentally established temperature dependences of τs and τt and from the theoretically known one of τp (=CRSS if the SiO₂-particles are the only strengtheners present), the function τt(τs,τp) has been derived: τt=(τks+τkp)1/k, with k≈1.8. This result is at variance with a linear relationship suggested earlier by Ebeling and Ashby [Phil. Mag. 13 (1966) 805]. The bearings of the present findings on the evaluation of experimental data on dispersion strengthening are evident.