For the Thomson scattering diagnostic in the ASDEX Upgrade tokamak, new transient recorders for acquiring the time evolution of the scattering pulses are used. Instead of integrating over the scattering pulse, as performed by the usually applied charge-sensitive analogue-to-digital converters (ADCs), a non-Gaussian pulse shape is fitted to the measured scattering signal. Both in this fitting procedure and in determination of the electron density and temperature from the scattering signals, correlated noise is taken into account. The number of outliers due to perturbations of the scattering signal is substantially reduced and the resulting electron density and temperature values are of higher accuracy than those that were obtained with the evaluation method based on charge-sensitive ADCs. The minimum electron density, detectable with a signal-to-noise ratio of 1, is now at ne = 0.75 × 1018 m−3, which is a factor of 3 lower than that obtained with the evaluation based on the integration over the scattering pulse.