[en] Two powerful and complementary techniques are described that could be used advantageously at LAMPF II for studying short-lived nuclei far from the line of beta stability, produced through fission or spallation reactions. The ground-state and excited-state properties of such nuclei are of great interest to nuclear model theorists. One of the proposed techniques utilizes a new type of recoil time-of-flight spectrometer that would enable the direct mass measurement of some 50 new neutron-rich isotopes in the light mass (A < 70) region with accuracies of 50 keV to 1 MeV. The second technique involves a so-called helium-jet-coupled mass separator, which would facilitate mass and spectroscopic measurements on short-lived isotopes of a number of elements (for example, refractory metals) that cannot be studied at any of the existing or planned on-line mass-separator facilities