We propose a scheme for universal quantum computing based on Kramers rare-earth ions. Their nuclear spins in the presence of a Zeeman-split electronic crystal field ground state act as "passive" qubits that store quantum information. The "active" qubits are switched on optically by fast coherent transitions to excited crystal field states with a magnetic moment, and the magnetic dipole interaction between these states is used to implement controlled NOT (CNOT) gates. We compare our proposal with others, noting particularly the much improved CNOT gate time as compared with a Si:P proposal, also relying on magnetic dipole interactions between active qubits, and rare-earth schemes depending on the dipole blockade for qubits spaced by more than of the order of 1 nm.