Abstract: The authors have undertaken an investigation of techniques for evaluating prompt fission-neutron spectra (PFNS) and their covariances that began during a visit by two of them (Smith and Neudecker) to the IAEA-NDS, Vienna, Austria, in July 2013. This collaboration has continued to the present time, with on-going evolution in our understanding of various technical issues associated with PFNS data evaluation. This paper does not attempt to provide a comprehensive review of other recent studies in this field, including those having to do with neutron spectrum evaluation methods or with evaluations for specific actinides such as 235U, 239Pu, or 252Cf. This investigation has focused on several aspects of the evaluation of PFNS shape data and corresponding covariances directly in PFNS space, with an emphasis on the issue of PFNS data scaling. Considerable attention has been given in the present work to examining techniques for preparing diverse normalized and non-normalized data from nuclear modeling and experiments, as required for their combined inclusion by either simple linear least-squares (SLS) or generalized linear least-squares (GLS) evaluation procedures. Technical issues associated with normalizing non-normalized PFNS evaluated spectrum shapes and corresponding covariances to satisfy constraints on spectral shapes as well as their covariance matrices that are dictated by normalization have been examined in this investigation. Methods for computing PFNS average neutron energy and its uncertainty from evaluated PFNS shape data and corresponding covariances are also discussed in this paper.