Simply select the associated anchorPoint, get the Scale Tool (the center of transform will be at the location of the anchorPoint) and scale it.
When using the Convert tool, of course, the normal (and often infuriating) behavior is for both curve handles to extract at the same time.
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Apologies for my bad advice. Subtract ten points.
Thanks, JET. I was trying to use the Direct Selection tool, and didn't think of using the Scale tool.
Thanks for letting me know about the Better Handles plug-in. Although not necessary to scale the direction lines, it looks like a useful plug-in.