I would tread slowly here. Compared to generic cable the 6003 is more revealing. It could possibly be telling you about something else in your system is off in the highs (CD, Amp, other interconnect cables, etc).
What is the rest of your system composed of? Going further up the ladder is only going to make things more revealing. All cables need some burn-in. I still use the 6003 in a high-end receiver based system in my work office.