  We prove that relational structures admitting specific polymorphisms (namely,
canonical pseudo-WNU operations of all arities $n \geq 3$) have low relational
width. This implies a collapse of the bounded width hierarchy for numerous
classes of infinite-domain CSPs studied in the literature. Moreover, we obtain
a characterization of bounded width for first-order reducts of unary structures
and a characterization of MMSNP sentences that are equivalent to a Datalog
program, answering a question posed by Bienvenu, ten Cate, Lutz, and Wolter. In
particular, the bounded width hierarchy collapses in those cases as well.
