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Can I ask why you don't want to use a JTable?

Yeah, I was going to point out that simply using tabs probably won't accomplish your goal of alignment. If I were you, I might even use a renderer that puts each cell in its own JLabel, then add them...

Interesting find, and thanks for creating the SSCCE. Apparently other people have dealt with this issue. I googled "java tabs in jlist" and found the following solution:
Tab list renderer :...

Like I said, it would be nice to see an SSCCE of what you're actually doing. Otherwise we're just guessing.

I'd be curious to see an SSCCE that demonstrates this. What happens if you only place one tab between the text? What do you want to happen instead of what's happening now?