A set of algorithms is presented that facilitates the evaluation of super continuum laser absorption spectroscopy (SCLAS) measurements with respect to temperature, pressure and species concentration without the need for simultaneous background intensity measurements. For this purpose a non-linear model fitting approach is employed. A detailed discussion of the influences on the instrument function of the spectrometer and a method for the in-situ determination of the instrument function without additional hardware are given. The evaluation procedure is supplemented by a detailed measurement precision assessment by applying an error propagation through the non-linear model fitting approach. While the algorithms are tailored to SCLAS, they can be transferred to other spectroscopic methods, that similarly require an instrument function. The presented methods are validated using gas cell measurements of methane in the near infrared region at pressures up to 8.7 bar.