This paper reviews measurements of fission cross sections of short-lived nuclear states, summarizes the formidable experimental difficulties involved, and suggests novel methods of overcoming some of those difficulties. It is specifically concerned with the two such states that have been well characterized, the J = 1/2+ (26-min) isomeric 235mU and the J = 1- (16-h) ground state (shorter lived than the isomer) 242gsAm, and with measuring their fission cross sections at mega-electron-volt energies. These measurements are formidably difficult, partly because of the need to produce, separate, and collect the short-lived states before they decay and partly because of their comparatively small fission cross sections at these energies. This paper presents quantitative calculations of the efficiency of advection of recoiling 235mU isomers by flowing gas in competition with diffusive loss to the surface containing the mother 239Pu, and it reports the initial development and evaluation of some of the methods that must be developed to make the experiments feasible.