THERE are two different types of missing (dark) matter: the unseen matter needed to explain the high rotation velocities of atomic hydrogen in the outer parts of spiral galaxies1,2, and the much larger amount of (non-baryonic) matter needed to prevent the universe from expanding forever1 (producing either a `flat' or a `closed' Universe)3. Several models have been proposed to provide the dark matter required within galaxy haloes for a flat universe, of which cold dark matter (CDM) has proved the most successful at reproducing the observed large-scale structure of the Universe4-6. CDM belongs to a class of non-relativistic particles that interact primarily through gravity, and are named dissipationless because they cannot dissipate energy (baryonic particles can lose energy by emitting electromagnetic radiation). Here I show that the modelled small-scale properties of CDM7-9 are fundamentally incompatible with recent observations10-13 of dwarf galaxies, which are thought to be completely dominated by dark matter on scales larger than a kiloparsec. Thus, the hypothesis that dark matter is predominantly cold seems hard to sustain.