The effects of large carbon enrichments in static stellar envelopes were investigated, using new Los Alamos opacities (including low-temperature carbon and molecular opacities) and including carbon ionizations. To search for the production of low-mass, low-luminosity carbon stars, detailed stellar evolutionary computations were carried out for a grid of low-mass stars of two different metallicities. The stars were evolved from the main sequence through all intermediate stages and through helium shell flashes on the asymptotic giant branch. The effects of the latest nuclear reaction rates, the new Los Alamos opacities, Reimers-type wind mass loss, and detailed treatment of convection and semiconvection were investigated. Two low-luminosity carbon stars were achieved, in excellent agreement with observations. Conditions favoring dredge-up (and thus carbon star production) include a reasonably large convective mixing length, low metallicity, relatively large envelope mass, and high flash strength. Mass loss was of major importance, tending to oppose dredge-up; the total mass loss amounts inferred from observations suffice to prevent formation of high-mass, high-luminosity carbon stars.
Composition dependence of the important and widely-used Mc - L, Mc - Tb, and Mc - τif relations at low core mass was obtained; the first two of these differed significantly from extrapolations from higher-mass stars. The flash strength LmaxHe was not found to obey any such relation; this renders suspect certain computational short-cuts frequently used in the literature.
