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 galaxies(1,2), and the much larger amount of (non-baryonic) matter needed to prevent the universe from expanding forever(1) (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 Universe(4-6). 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 CDM(7-9) are fundamentally incompatible with recent observations(10-13) 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.