The interparticle breakage of fine feed fractions of quartz, zircon silicate, smelted corundum and silicon carbide is investigated by stressing a particle bed either once with a pressure between 600 and 1800 MPa or several times with a pressure of 100 to 700 MPa. The multiple compression is performed in a press unit with two piston pairs orientated perpendicularly to each other and acting alternatively. Each successive stressing, therefore, disaggregates the compacted bed of the preceding compression. The size-reduction depends only on the specific energy absorption and not on the pressure level, at which the energy is introduced. The data allows an estimate of the specific comminution energy without any machinery losses for producing a product with a wanted fineness characterized by the maximum particle size to be obtained. These results are much less than the energy consumption of stirred ball mills.