This paper highlights the advantages of not interpreting connections in a dependency tree as combinations between words but of interpreting them more broadly as sets of combinations between catenae. One of the most important outcomes is the possibility of associating a connection structure to any set of combinations assuming some well-formedness properties and of providing a new way to define dependency trees and other kinds of dependency structures, which are not trees but "bubble graphs". The status of catenae of dependency trees as syntactic units is discussed.