A new calculation scheme has been developed to improve the quality of covariance matrices of a-priori neutron spectra. A high quality covariance matrix is essential for guiding the adjustment of the a-priori calculated neutron spectrum to experimental dosimetry measurements in a physically realistic way. This new calculation scheme incorporates state-of-the-art hybrid deterministic/Monte Carlo methods and does not rely on prior knowledge of correlations between the different energy groups. The ADVANTG code was used to generate weight-windows for the full MCNP reactor model of the High Flux Reactor (HFR) in Petten, the Netherlands. This then allowed Total Monte Carlo (TMC) calculations to be performed with very low statistical uncertainties. A detailed demonstration of applying these covariance matrices to spectrum adjustment is also provided by utilising an algorithm adopted from the STAY’SL program. We have used the example of the HELIOS irradiation experiment performed at the HFR to demonstrate the approach here, but the flexibility of the method means it may be applied universally to neutron spectra calculated anywhere.