An intermediate Hamiltonian Fock-space coupled cluster method is presented. This method allows the use of large and flexible P spaces without encountering intruder-state problems. The larger P spaces enhance the accuracy of calculated transition energies by factors of 3–6, and make accessible many states which could not be handled by other CC methods. Examples given include the pilot calculation on Sc + levels, where accuracy increased by a factor of 4; element 114, where ionisation potentials show considerable increase relative to lighter group-14 atoms, due to relativistic stabilisation of the 7s and 7p1/2 orbitals; and a benchmark calculation of the electron affinities of the alkali atoms Na–E119, where results agree within 5 meV or better with known experimental values, providing a new reference value of 491±5 meV for the experimentally unknown EA of Fr.