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I’m actually about to dive into this similar situation, so I don’t have much experience yet, but have you seen the Slick2D class CanvasGameContainer?
Maybe it’s code will help you out. It’s what I plan to use to tackle the issue. It’s still an awt Canvas, which is still heavyweight, but maybe something in the class has accounted for that. I haven’t looked at it deeply.
Then again, my application is modal, so all the controls are on separate windows with the canvas getting its own JFrame.
Have you tried [icode]JPopupMenu.setDefaultLightWeightPopupEnabled(false)[/icode] ?