RadViz plots are commonly used to represent multidimensional data because they use the familiar notion of 2D points for encoding data elements, displaying the original data dimensions that act as springs for setting the x andy coordinates. However, this intuitive approach implies several drawbacks and produces misleading visualizations that can confuse the user, even while analyzing a single data point. The paper attacks this problem following the well known idea of changing the order of the dimensions and introducing ancillary visualizations to mitigate some of RadViz drawbacks. In particular, the paper defines the notion of point optimal disposition of the dimensions for a single data point, generalizes this concept to a set of data points, and proposes effective heuristics for dealing with the intractable problem of exploring all the (n-1)!/2 dispositions of the dimensions along the RadViz circumference. Additional views, visual quality metrics, and a circular grid superimposed on the RadViz complement the attribute reordering strategy and provide abetter understanding of the actual plot of the data elements.