I have one with no carpet and Chloe uses it all the time.  It's just a
wooden post on a large wooden round disk, but my husband made the whole
thing.  Chloe is the only one of the three to use it, though.  The others
prefer our bedroom carpet, although we've got sisal on the walls.

kili

I have one, but unfortunately it's made by a Finnish company. I don't
think they ship to the US (and their products are pretty expensive, not
to mention the cost of shipping overseas...).

Oh! I just looked for their website, but it's gone! I hope they haven't
gone out of business.

I don't have one that's completely carpetless, but two of them
are mostly sisal, with some carpet near the top. I used to have one
that was all carpet, and yes, I do remember the little pieces of
rug yarn all over the floor near the base of the post. :)

I moved the all-carpet one into an alcove where, for the time being
at least, I store mostly junk, so what's a few more rug yarns? In the
living room, I have two sisal-wrapped posts, with carpet at the top
and at the base. Those don't get too messy. But YMMV, apparently - I
guess your guys really like to tear out the pieces of carpet?

If you're handy, could you re-do your post with sisal rope. You'd
have to get a good box-cutter to remove the carpet (it's easy to cut
carpet samples with a box-cutter - I have done this). Sisal rope is
not expensive and you can buy it at any place that has a hardware
department. I think I got my last roll at Walgreen's.

Then you need a good staple gun. The staples have to be long enough
to go through the sisal rope and then go deeply enough into the post
to hold. And the staple gun has to be big enough for those staples.
(I say this because I have a staple gun, but only short staples fit
into it, not long enough for building a cat scratching post. Note to
self: buy bigger staple gun.)

But other than that, it's not really that difficult. I've replaced
sisal on scratching posts, once it's gotten all torn and "frizzy".

Good luck.

Here are some scratching posts that meet your requirements.  At the same
time, I want to warn you that it is sometimes a mistake to try to divert
cats to a different scratching material.  Cats have definite preferences,
and they sometimes will not make the transition.  So, be sure to keep your
old post for awhile until you are sure your cats will use the new one.  (I'm
sure you would rather have tufts of scratching post material than tufts of
your furniture scattered around!)  Actually, I have a scratching post in
every room except the kitchen and bathrooms, and my cats do show obvious
preferences for some.  Their favorites are always the sisal rope posts.
Over time, they will also get rather scroungy-looking, of course, but they
do the job they are intended for.

My cats like this one, but not as much as the posts with sisal "rope" wound
around the post.  It is made of woven sisal material.
http://www.catsplay.com/smartcat_post.php3

This one is also made of woven sisal fabric:
http://www.purrfectpost.com/

Here is an ad for a natural cedar scratching post (32" high).  I have not
used this one, but it looks intersting:
http://www.naturalscratch.com/

This location offers some very tall scratching posts.  As I'm sure you know,
it's important for a post to be *tall* (to encourage stretching) and
*sturdy/heavy* (to prevent the post from toppling over and possibly scaring
the cat).  Again, I have never used this company, but these are the tallest
commercially-made posts I have seen advertised:
http://www.angelicalcat.com/c1_scratch_posts.shtml

Here is a post that looks almost identical to the cedar post listed above:
http://www.lovethatcat.com/cat-scratching-post.html
Incidentally, this location also has cat trees made by the company where I
bought two for Holly and Duffy.  The woman who owns this company had seen
some of my pictures and wrote to ask if she could include one on her web
site.  I gave my permission, so Holly and Duffy are now "web site stars."  I
do not have any other connection with the company, and I gave my permission
to use the pictures without compensation (other than a cat video that they
sent me).  Here are Holly and Duffy as advertising models:
http://www.lovethatcat.com/cat-tree-3.html

MaryL

I suspect you might have to make your own.  As far as a post sans carpet
is concerned, I've often thought a nice piece of tree trunk, bark and
all, set at an angle, would be ideal.  (Of course, you'd have to treat
it with something so there were no uninvited critters - like termites -
still in residence.)