Twitchy steering fix?

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I bought an Independent Fabrication steel Crown Jewel used - it's a
stock frame (non custom) with an IF steel fork - straight blades.

It has very "twitchy" steering when I'm in a descending tight corner.
I tend to oversteer in those situations. The bike feels like it pulls
into the turn to a point where I'm about to loose control.

To compare I have a Trek 5200 (new in 2000, 60cm frame) that I use the
same wheels on and has almost the same fit. The only major difference
I can find with my tape measure is the IF has 42cm handlebars while the
Trek has 44cm. I never notice my cornering problem when I'm on the
Trek.

Anyone have opinions on how I can "smooth out" (or slow down, or make
it less responsive) the high speed cornering on the IF bike? Will
different forks make a difference - any advise on what to go to? Any
other changes that make make a difference in handling?

Thanks,

Al Sharff