During the last couple of decades of work on the Σ–D (radio surface brightness to diameter) relation for supernova remnants (SNRs), it has been generally accepted that no single Σ–D relation can be constructed for all SNRs. However, it may still be possible to construct the relations for some classes of SNRs. In our previous paper we analysed Σ–D relation(s) for remnants in the dense environments of molecular clouds. The aim of this paper is to examine, in the same context, a class of oxygen-rich SNRs, and to extend the analysis to remnants evolving in lower-density interstellar media, namely Balmer-dominated SNRs. We have obtained good relations with certain similarities to our previous findings – similarities that emphasize, again, the role of ambient density in the evolution of SNRs.