  It is obtained a natural generalisation of Uspenskij's selection
characterisation of paracompact $C$-spaces. The method developed to achieve
this result is also applied to give a simplified proof of a similar
characterisation of paracompact finite $C$-space obtained previously by Valov.
Another application is a characterisation of finite-dimensional paracompact
spaces which generalises both a remark done by Michael and a result obtained by
the author.
