Laminar flows in annular tubes can be encountered in industrial situations. In order to improve static and continuousmixers or multifunctional heat exchangers, several ways have been investigated. In the present article, two alreadywell-known kinds of passive enhancement devices are set on a laminar annular flow and numerically studied. Alter-nate elliptic wall deformations are applied to the external wall as the internal wall is swirled. These geometricalperturbations both create secondary flows that are in mutually orthogonal directions. Their combination is numeri-cally evaluated in this paper and is found to lead to a significant increase of the mixing. A nearly uniform mixing iseven achieved for a reduced tube length as shown by considering scalar mixing for different inlet configurations. Theanalysis, based on Lagrangian tracking and Poincaré sections, shows that the mixing enhancement can be explainedby the formation of zones of chaotic advection in the flow.