Excited double-core-hole states of isolated water molecules resulting from the sequential absorption of two x-ray photons have been investigated. These states are formed through an alternative pathway, where the initial step of core ionization is accompanied by the shake-up of a valence electron, leading to the same final states as in the core-ionization followed by core-excitation pathway. The capability of the x-ray free-electron laser to deliver very intense, very short, and tunable light pulses is fully exploited to identify the two different pathways.