It is known that the diffusion constant of the banded areas of the cigarette paper is an important parameter for achieving compliance with regulations regarding the ignition strength of cigarettes. Nevertheless, in many cases, the diffusion constant does not show a good correlation with ASTM E2187 test results. The hypothesis of the present investigation is that this is because the diffusion constant of the banded areas is measured under standard conditions, that is at 23 °C, while for a good performance in the ignition strength test the band has to inhibit the diffusion of oxygen to the glowing cone at much higher temperatures, when the paper and the band material are already partially decomposed. To investigate this, three-banded cigarette papers with the band material containing a cellulose derivative, starch and a starch derivative, respectively, were heated to temperatures between 170 °C and 290 °C for times between one minute and two hours. The diffusion constant of the bands was measured afterwards and a mathematical model was derived from the data to describe the thermal degradation of the bands. This model was combined with a mathematical model of a smouldering cigarette for numerical simulation. The influence of the degradation speed on the self-extinguishment was simulated and compared to a set of experimental data obtained from cigarettes produced from the three-banded cigarette papers. It could be shown that the diffusion constant of the thermally decomposed bands on the cigarette paper is a far better predictor of ASTM E2187 performance than the diffusion constant of the banded areas under standard conditions. The model also explains how the band material influences the test results, and can be used to design papers for FSC cigarettes.