A new concept for direct mass measurements of short-lived nuclei with an electrostatic time-of-flight mass spectrometer is described. The spectrometer can be coupled to an in-flight separator such as SHIP or FRS via a gas stopping cell and a gas-filled linear Paul trap. The time required for mass measurement is of the order of a few milliseconds allowing one to investigate nuclei with these short half-lives. A mass-resolving-power m/Δm _FWHM=50 000 has been reached. First results of the range-focusing technique are presented, which is under development for the efficient stopping and extraction of relativistic exotic nuclei.