Sounds like you answered your question.

I think it's the same frame as 2015 P2...dimension wise, and the 28 was just too close to take out on the road for me. 25s with 21mm internal HED Jet is pretty wide and very doable.

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DFRU - Detta Family Racing Unit...the kids like it and we all get out and after it...gotta keep the fam involved!

In my experience it heavily depends on how much your rear wheel flexes. You can always back the dropout screws out, but the side of the tires can rub the stays while climbing, turning, or sprinting if the tires are too big. I stick with 25's on the back with most rim brake wheels. 23's for some.

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Benjamin Deal - Professional - Instagram - TriRig - Lodi Cyclery
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If a "2013 Cervelo P3" is the "Fabian Cancellara" style frame (CSC Team years), then 28mm's are never going to fit

Is there a particular reason you want to put 28mm tire? 25mm is already pretty fast and comfortable.

After trial and error, I can confirm that 28mm tires will fit on a 2013 P3 Cervelo.

I bought new Continental 28-32MM tubes and a Continental Grand Prix 5000 Tires. The front tire was easy to install, with no changes required. For the rear, I had to "back out" the droupout screws and Voila, it fits with no rubbing on the frame. For reference, my wheelset is Rolf.

The next challenge will be to ride the bike on hills/mountains to see if the wheel/tire clearance is enough to cover the flex. I'm 99% confident that this will work.

The good news is that if you have an old rim brake tri bike, you may be able to upgrade to 28mm tires (depending on manufacturer of the bike, wheels, tires, etc.), but it is feasible.

You should get latex tubes.

I take exception to the "antique" term.

My 2010 P3c is no more antique than I am.......oh hang on