We present three extensions to parallel coordinates that increase the perceptual salience of relationships between axes in multivariate data sets: (1) luminance modulation maintains the ability to preattentively detect patterns in the presence of overplotting, (2) adding a one-vs.-all variable display highlights relationships between one variable and all others, and (3) adding a scatter plot within the parallel-coordinates display preattentively highlights clusters and spatial layouts without strongly interfering with the parallel-coordinates display. These techniques can be combined with one another and with existing extensions to parallel coordinates, and two of them generalize beyond cases with known-important axes. We applied these techniques to two real-world data sets (relativistic heavy-ion collision hydrodynamics and weather observations with statistical principal component analysis) as well as the popular car data set. We present relationships discovered in the data sets using these methods.