A process for making a detergent tablet by forming a disintegrating agent by compacting cellulose or a cellulose derivative, forming disintegrating agent particles comprising the disintegrating agent, dry mixing a washing- or cleaning-active substance and an amount of the disintegrating agent particles effective to rapidly dissolve or disperse the composition in water, and shaping the resulting mixture into a tablet. The disintegrating agent particles have a particle size distribution of less than 10% by weight smaller than about 0.2 mm particle size and no more than 1% by weight of dust-fine particles.