Many proteins and peptides are increasingly being recognised to contain unfolded domains or populations that are key to their function, whether it is in ligand binding or material assembly. We report an approach to determine the secondary structure for proteins with suspected significant unfolded domains or populations using our neural network approach SOMSpec. We proceed by derandomizing spectra by removing fractions of random coil (RC) spectra prior to secondary structure fitting and then regenerating α-helical and β-sheet contents for the experimental proteins. Application to bovine serum albumin spectra as a function of temperature proved to be straightforward, whereas lysozyme and insulin have hidden challenges. The importance of being able to interrogate the SOMSpec output to understand the best matching units used in the predictions is illustrated with lysozyme and insulin whose partially melted proteins proved to have significant βII content and their CD spectrum looks the same as that for a random coil.