I have been making rods for 2 years as a "commercial enterprise", but have been making rods for self, family & friends for nearly 50 years.
In the last 2 years I have made more than 2 dozen rods with pieces from 1-1/2 inch long to 14 inches long. I have purchased handles and have made handles from cork rings. More than 50% of the time the reamed hole will be off-center. I have reamed by hand, using a reamer in an electric drill and using the reamer chucked into my lathe. My reamers are varying size from 1/4-inch diameter to more than 5/8 inch diameter. As mentioned in other posts, I sometimes run the reamer counter clockwise as well as forward. I am at my wits end on ensuring a centered hole, even on a 2-inch butt or fore-grip.

One thing I have not tried is tapered round files. I just "found" that idea today while searching the forum for the off-centered reamed hole.

Please let me have your ideas.

The Flex Coat cork boring bits will solve your problem completely. You can buy them ready made, or buy the kit to make your own. You can enlarge the bore to a near perfect, and centered fit in about 5 seconds, and then finish off the taper with a reamer, in another 5 seconds.

Beyond that, when you ream, the reamer must be nearly as large in OD as the grip bore is in ID. If you're trying to enlarge a bore with a reamer that is undersized by much, you tend to get things off center. Another thing that will help is ditching the drill. Cork reams very easily and you can exert a bit more craftsmanship by hand than with a power tool in this instance.

...................

Or, allow the cork you are reaming to "slip" a little at a time as you are power reaming.
That will change the pressure to a different axis as you are reaming thru.
Kinda like hand filing with a round file and turning the cork a few degrees every few strokes to help keep it centered.
Hope this helps.

Best wishes,
Ron Schneider
Schneider's Rod Shop
Mountain Home, Arkansas
[www.schneidersrods.com]
mtnron40@yahoo.com
870-424-3381

x10 on Ron's comments.
I use a drill with a round file or a reamer chucked into the drill. If I am using the circular file, I run the drill backwards to prevent the file from splitting the cork.

But, Ron has it right, let the object that you are reaming, fliling or boring slip a bit from time to time in your hand. For this purpose, I wear a cloth glove on my holding hand. The cloth glove lets the object slip when needed, but holds tight otherwise. Also, the glove keeps the hand from being burned by the slipping cork.

Also, reverse the direction of reaming or boring - until you are at the limit of boring from that size. By boring from both ends, this also helps to keep the object centered as well.

Be safe

On spinning rods, you can taper the cork to the OD of the reelseat, removing the offcenter.

I do how Rod suggested all the time he is on
be easy do not force the reaming
ream for several secounts Stop turn the material ream again turn and ream

When You get cloes to the size
I take the reamer off the drill or power
And then Finish buy hand reaming
Hold the reamer and turn the handle for a end fit

Bill - willierods.com

As Bill pointed out, I use a cloth glove to let me slip the grip without burning my hand.
I generally am letting the grip slip most of the time, so that the grip is turning a bit as I bore or ream with the drill and file or reamer. It does a very nice job of keeping the bore on center.

Be safe

Ditto on letting the grip spin in your hand. I also hold the drill vertically to distribute the weight more evenly around the inside of the grip while reaming.

Don Campbell
don@sensorfishingrods.com

Thanks to all of you. I have not been letting the work-piece rotate in my hand. I will assemble some cork handle practice pieces try from there.