We determined some basic properties of stars that produce spectacular gamma-ray bursts at the end of their lives. We assumed that accretion of the outer portion of the stellar core by a central black hole fuels the prompt emission and that fall-back and accretion of the stellar envelope later produce the plateau in the x-ray light curve seen in some bursts. Using x-ray data for three bursts, we estimated the radius of the stellar core to be approximately (1 - 3) x 10(10) cm and that of the stellar envelope to be approximately (1 - 2) x 10(11) cm. The density profile in the envelope is fairly shallow, with rho approximately r(-2) (where rho is density and r is distance from the center of the explosion). The rotation speeds of the core and envelope are approximately 0.05 and approximately 0.2 of the local Keplerian speed, respectively.