The bitopological unstability of RR-pairwise paracompactness in
presence of pairwise Hausdorff separation axiom is caused by a
bitopological property which is much weaker and more local than
RR-pairwise paracompactness. We slightly generalize some
Michael's constructions and characterize RR-pairwise
paracompactness in terms of bitopological θ-regularity, and
some other weaker modifications of pairwise paracompactness.