I just purchased an 05 Elise a few weeks ago. The day after I bought it I noticed that once the engine warms up I get a squealing on deceleration. Usually between 3500 and 2900 RPM. It sounded a lot like a bad belt. So I took the belt off, looked okay but figured it's got 40k miles on it. It may be stretched over the years. Checked the tensioner pulley and had a little play. Checked the idler pulley and had a lot of play. All the rest seemed fine. So I replaced the belt and both pulleys. Took it for a drive only to hear it again! I've heard of the exhaust squealing but no one has videos for me to compare. And I can't find anything cracked.
Did a search and found people saying it may be the clutch but it does the same thing in neutral under no load around the same rpm.
I'm kind of flustered at this point. The belt is tight. Not a hint of play.
Mods include a intake and the janspeed fatback/muffler.
The cat and headers are factory. I'll try and get a video as soon as I can get another person to join me in my garage.