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This manuscript presents an ultrafast-laser-absorption-spectroscopy (ULAS) diagnostic capable of providing calibration-free, single-shot measurements of temperature and CO at 5 kHz in combustion gases at low and high pressures. Additionally, this diagnostic was extended to provide 1D, single-shot measurements of temperature and CO in a propellant flame. A detailed description of the spectral-fitting routine, data-processing procedures, and determination of the instrument response function are also presented. The accuracy of the diagnostic was validated at 1000 K and pressures up to 40 bar in a heated-gas cell before being applied to characterize the spatiotemporal evolution of temperature and CO in AP-HTPB and AP-HTPB-aluminum propellant flames at pressures between 1 and 40 bar. The results presented here demonstrate that ULAS in the mid-IR can provide high-fidelity, calibration-free measurements of gas properties with sub-nanosecond time resolution in harsh, high-pressure combustion environments representative of rocket motors.