Calling all lawyers: about perjury

It's about perjury.

"Perjury" is a term that's being used in connection with the Libby indictment. It's often loosely defined as "lying under oath."

But it turns out that lying under oath is a necessary, but not sufficient, element of perjury. I remember learning this way back (seems like decades ago, doesn't it?) during Clinton's impeachment. It turns out that the lie involved in perjury must be about a fact material to the case.

Take a look; here's the "material" part:

a) Whoever under oath (or in any declaration, certificate, verification, or statement under penalty of perjury as permitted under section 1746 of title 28, United States Code) in any proceeding before or ancillary to any court or grand jury of the United States knowingly makes any false material declaration or makes or uses any other information, including any book, paper, document, record, recording, or other material, knowing the same to contain any false material declaration, shall be fined under this title or imprisoned not more than five years, or both.

"Material" in this context means "relevant to the case at hand."

So my question is actually quite simple (and please don't call me a simpleton for asking it): can someone be indicted for perjury--that is, lying about a material element of a case--when there is no other case? If perjury ends up being the only charge in a long-term investigation, what case is the lie material to?

The answer, of course may be "the one that was suspected, but for which not enough evidence was found to sustain an indictment." Doesn't this seem a bit strange, legally speaking?

Of course, one could argue that, even when there ends up being no primary case, the secondary case--perjury--still needs to be prosecuted to make it clear that lying under oath about a fact that would have been material had the case gone to trial is a serious offense.

But I'm wondering, if that's true: how often are such cases actually prosecuted? And under what circumstances?

All you lawyers out there, please feel free to comment.