Researchers and users are well aware of the difficulties related to finding an appropriate configuration of the axes mapping attributes in multidimensional visualization techniques, particularly in visualizations that show a large number of attributes simultaneously. We address this problem with a simple strategy that offers both dimension ordering and dimension reduction. Dimension ordering is based on attribute similarity heuristics, and the basic rationale is extended to support dimension reduction. We discuss the performance of our algorithms and present some results of their application to several data sets. The algorithms improve the capability of visualization techniques to segregate clusters present in the data and reduce the visual clutter aggravated by arbitrary distributions of the axes.