I had some problems riding no handed on my bike, even though like the OP I could ride several miles including corners without even a twinge of need to hold the handlebars.
I assumed it was related to my suspension fork, but I tried today, and I had a much easier time. I thought that in my case moving from egg shaped rider toward normal proportioned rider was helping. But, after reading the comment about the handlebars being straight, I think that was part of it. A couple of months ago I straightened the bars that had been irritating me for quite some time (but they were close enough that I didn't think it would bother me.
Next time I ride my Univega I'll have to see how I do...
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Slow Ride Cyclists of NEPA
People do not seem to realize that their opinion of the world is also a confession of character.
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