White dwarfs grow as the cores of red giants and, in particular, carbon-oxygen white dwarfs grow in asymptotic giant branch (AGB) stars. The evolution of an AGB star is a competition between growth of the core and loss of the stellar envelope, typically in a wind. It is complicated by thermal pulses driven periodically by unstable helium shell burning. Dredge up following such pulses delays core growth. The compression at the center of a cold carbon-oxygen core means that carbon ignites when it reaches a mass of 1.38 M⊙. This begins the familiar thermonuclear runaway of the Type Ia supernova (SN Ia). At higher temperatures carbon can ignite more gently and burn mostly to neon to leave a core rich in oxygen, neon and magnesium. Such cores can go on to collapse to neutron stars with a release of only neutrinos. Accepted mass-loss prescriptions for giants mean that the range of masses of single stars that leave carbon-oxygen white dwarfs is somewhere from around 1 to 8 M⊙. We investigate how unusual mass loss, perhaps brought about by interaction with a binary companion, can radically alter the single star picture. Though population syntheses treat some possibilities with various prescriptions, there is sufficient doubt over the physics, the observations, and the implementation of mass loss and binary interaction that there is scope for several more unusual progenitors of carbon-oxygen white dwarfs and hence SNe Ia.