Newly generated frequencies during bulk continuum generation with femtosecond pump pulses do not fluctuate statistically and show strong correlations in spectrum and time. When a femtosecond continuum is used as probe light for transient spectroscopic measurements, these correlations result in a seemingly low noise level but large-scale pseudo-structures that obscure the interpretation. We investigate the correlations for continua generated in YAG and calcium fluoride plates and incorporate the results into the design of our pump–probe setup. The high degree of correlation to the next pulse is utilized through chopping of the pump and referencing between successive laser shots. To suppress the adverse effect of the high degree of correlation to other wavelengths, we extend the detection by multichannel referencing with a second camera. The combination of both referencing schemes renders a precise spectral calibration unnecessary and increases the sensitivity of our spectrometer by a factor of 5 down to 20 μOD. This is already very close to the shot noise limit. To demonstrate the improvements, we present and discuss measurements on two different molecular solutions.