Carbon 1s photoelectron spectra for CF4 and CO have been measured at several photon energies near the carbon 1s threshold. The spectra have been analyzed in terms of the vibrational structure and the natural linewidth. For CO the vibrational structure shows evidence for anharmonicity in both the energy spacing and the intensity. Analysis of the results using an anharmonic model gives an equilibrium bond length for core-ionized CO that is 4.85 pm shorter than that of neutral CO. For CF4, the vibrational structure is very weak, and the analysis shows that the change in equilibrium CF bond length upon ionization is no more than 0.54 pm. Ab initio theoretical calculations give results in accord with these bond-length changes. The unusually small bond-length contraction in CF4 can be understood in terms of nonbonded fluorine-fluorine repulsion. The natural linewidth for core-ionized CO, 95+/-5 meV, is essentially the same as that of CH4. This result is in contrast with expectations based on the one-center model of Auger decay and earlier predictions based on semiempirical molecular orbital theory. More recent calculations indicate, however, that there is only a small difference between CO and CH4, in agreement with the observed result. For CF4, the natural linewidth is 77+/-6 meV. This value differs from that for CH4 in the direction expected from the electronegativities of hydrogen and fluorine, but is greater than the prediction based on semiempirical theory. The natural linewidth for CO with a carbon 1s electron excited to the 2pi resonance is 83 meV, which is significantly less than is found for core-ionized CO. Although this difference is supported by theoretical calculations, the direction of the difference is counterintuitive. An overview is presented of the current state of experimental and theoretical knowledge on carbon 1s linewidths.