I bought a MkIII Sprite last year and was amazed with how bad it was once I got 
it out on a dry day.  It did what you are describing, and new shocks cured its 
ills.  I bought extra firm for good measure.
gmari@optonline.net wrote:
> OK folks, I need some advice.
>
> For the past year my low mileage unrestored MKII Sprite (948) has had a 
>horrible swaying problem.  Last year it nearly cost my son and I our lives.
> Even at the slowest of speeds any left and right movement of the steering 
>wheel causes the front end to sway horribly.  I replaced the bushing with 
>poly...and installed an anti sway bar (thanks Frank).  These resulted in 
>minimal improvement.
> 1.  The car does not bounce up and down over bumps
> 2.  The tires are Yokohama 180/155's
 
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