A novel approach based on the projection of the Penning-trap ion motion onto a position-sensitive detector opens the door to very accurate mass measurements on the ppb level even for short-lived nuclides with half-lives well below a second. In addition to the accuracy boost, the new method provides a superior resolving power by which low-lying isomeric states with excitation energy on the 10-keV level can be easily separated from the ground state. A measurement of the mass difference of ^{130}Xe and ^{129}Xe has demonstrated the great potential of the new approach.