The long-standing puzzle of low C-12/C-13 in low-mass red giant branch (RGB) stars, and the more recent puzzle of low O-18/O-16 ratios in asymptotic giant branch (AGE) stars and in circumstellar Al2O3 grains preserved in meteorites, can be resolved by deep circulation currents below the bottom of the standard convective envelope. These currents transport matter from the nonburning bottom of the convective envelope down to regions where some CNO processing can take place (''coal bottom processing''). Modeling circulation with separate downward and upward streams, we found that, to resolve both discrepancies, the base of the extra mixing had to reach a temperature T-p close to that of the II-burning shell, namely, Delta log T approximate to 0.17 from the base of the H-shell for both RGB and AGE stars. While the envelope composition depends sensitively on T-p, it is insensitive to the speed or geometry of mixing. This indicates that our stream circulation model is generic, so that more sophisticated mixing models with the same T-p would yield similar results. On the AGB, our models predict that stars with low O-18/O-16 can be either S or C stars but must have low C-12/C-13 (similar to 4) and elevated N-14. Cool bottom processing also destroys He-3, so that galactic (D + He-3) decreases with time; this removes the strongest lower limit on the baryon density Omega(b) from big bang nucleosynthesis models.