ate studies(2) and fusion energy research(3,4). Laser-driven implosions of spherical polymer shells have, for example, achieved an increase in density of 1,000 times relative to the solid state(5). These densities are large enough to enable controlled fusion, but to achieve energy gain a small volume of compressed fuel (known as the 'spark') must be heated to temperatures of about 10(8) K (corresponding to thermal energies in excess of 10 keV). In the conventional approach to controlled fusion, the spark is both produced and heated by accurately timed shock waves(4), but this process requires both precise implosion symmetry and a very large drive energy. In principle, these requirements can be significantly relaxed by performing the compression and fast heating separately(6-10); however, this 'fast ignitor' approach(7) also suffers drawbacks, such as propagation losses and deflection of the ultra-intense laser pulse by the plasma surrounding the compressed fuel. Here we employ a new compression geometry that eliminates these problems; we combine production of compressed matter in a laser-driven implosion with picosecond-fast heating by a laser pulse timed to coincide with the peak compression. Our approach therefore permits efficient compression and heating to be carried out simultaneously, providing a route to efficient fusion energy production.