keywords in <hx>, but not in page body

does Google penalize this?

[RoySpencer]

The nature of our pages is such that our main keywords are in <h1> and <h2> headings, but zero to only one or two uses of those same keywords are in the content under the <h2> headings. Does anyone think Google penalizes for having few-to-zero keywords under the <h2> headings? Should I just remove the <h2>'s and let those keywords be content under the <h1> keywords?

[caveman]

There are other factors that have an influence in the example you provide, and also you don't say whether you're using the same kw's in h1 and h2.

Why not test variations on different pages/sites? Then you'll know for sure.

[RoySpencer]

Thanks for the response, caveman. The <h1> and <h2> tags all have the main keyword in common, but not others (eg. "widget information"; "widget types"; "widget history").

I'll think about how to do what you have suggested..the nearly-duplicate pages will have to be on the same website, otherwise other factors (e.g. inbound links, PR) are going to affect their different SERPs positions, too.