Recently, Brown et al. [J. Phys. Chem. A, 2000, 104, 7044] demonstrated the potential of cavity ringdown spectroscopy (CRDS) for investigating the kinetics of fast chemical reactions occurring on the same time scale as the ringdown. Based on an approach referred to as Simultaneous Kinetics and Ringdown (SKaR) model, they were able to determine reaction rate constants from the non-exponential ringdown profiles that arise from the convolution of the concentration change and the ringdown. However, non-exponential ringdown curves are also observed without any reactions when radicals are detected with absorption linewidths comparable to or narrower than the bandwidth of the probe laser. We present an extended SKaR model (eSKaR) that takes this bandwidth effect into account and allows us to extract rate constants from non-exponential ringdown profiles originating from a convolution of the bandwidth effect and the kinetics. The investigation of the rate constant for the fast reaction SiH2 + O2 → products (R1), which has been measured at total pressures in the range 2.5 mbar ≤ p ≤ 350 mbar with argon as inert buffer gas, serves as an example for its application. A pressure independent rate constant of k1(295 K) = (9.9±1.9)· 1012 cm3/ (mol s) was obtained.