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My road bike comes with 25 tires. They both seem to be slick smooth ones with little resistance. Recently I had couple of punctures in the rear and I decided to change the rear tire to a 23 which was more puncture resistant and better grip.

Is there a problem in using 23 in the rear and 25 in the front?

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No problems that I'm aware of. I use a 32 on the back with a 28 in the front. – Kibbee May 17 '14 at 15:42
No problem as such, you might find you have better control if the wider tyre is at the back but I doubt there's much in it. – PeteH May 17 '14 at 16:09
The difference between 23 and 25 isn't even noticeable -- one manufacturer's 23 may be wider than anothers 25. (But note that there is little difference in the "grip" of standard road tires, whether smooth or with moderate tread. The majority of traction comes from simple friction between rubber and road surface, and an aggressive tread is often less efficient.) – Daniel R Hicks May 17 '14 at 22:33
While tread is generally useless on a road bike tyre, different tyres do use different rubber compounds with different coefficients of friction. Grip is more important on a front wheel, but most punctures are rear wheel, so while running narrower rear wheel is unusual, it's possible the tyres he happens to have make it the right choice. – armb May 19 '14 at 10:01
(Or, pedantically, tread pattern is useless, since slicks still have tread - e.g. refers to "grooves of the tread pattern" but just uses "tread". – armb May 19 '14 at 10:05
up vote 3 down vote accepted

There isn't a problem with it, though you may find your ride quality to go down a bit by moving to a smaller tire (but 23 and 25's don't really have much cushion to begin with so this won't matter too much). There is also a slight change in gearing due to the change in diameter of the tire. Generally though, I'd expect a bigger tire in the rear than in the front due to where you sit.

In general, you can mix tires so long as they go on the rims and clear the frame + brakes. Here is everything you want to know about tire sizing, including recommended rim widths for given tire widths.

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That tends to be the opposite to what riders usually run. If you are going to have different widths- its more normal to put the wider on the back tyre- rather than on the front. I run 23mm on the front and 25mm on the back. You put a lot more stress/effort/weight over the rear tyre than the front & hence why it tends to be this way around. There is nothing "wrong" with having it the other way around however :).

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