One was convicted of seven felony counts just days before the election. Another is under indictment for bribery after FBI agents found $90,000 cash in his freezer. And seven others are facing ethics questions that range from ties to lobbyist Jack Abramoff to failing to report taxable income on a Caribbean villa.

But that didn’t stop the members of Congress and the Senate from having successful election nights on Tuesday.

As we noted yesterday, Sen. Ted Stevens (R-AK) appears to be on his way to back to Capitol Hill despite being convicted last week of failing to disclose gifts from an oil contractor. Meanwhile, Rep. William Jefferson (D-LA) – whose “cold” cash was allegedly intended to bribe the vice president of Nigeria – easily won a Democratic runoff that was pushed back by Hurricane Gustav. Jefferson appears poised to win re-election against “four poorly financed opponents with scant name recognition.” (Jefferson’s case hasn’t gone to trial yet.)

So what causes the lawmakers to continue to win over voters?

“I’ve got to believe that the reason why is that they’ve developed this network of support that’s based on bringing business opportunities and earmarks to the community,” said Craig Holman, a campaign finance lobbyist for the watchdog group Public Citizen. “The more they develop a network in their communities, the more likelihood they can survive a criminal investigation or indictment.”

Holman noted that congressmen facing corruption charges have often had trouble getting re-elected; usually a shoe-in, Stevens is now “in the race of a lifetime,” he said.

ABC News has a roundup of how the suspect lawmakers fared on Election Day. Not all of them won. Rep. Tim Mahoney (D-FL), accused of paying off a mistress, lost his seat while Rep. Charlie Rangel (D-NY) – facing questions about the villa, rent-stabilized apartments, free parking and donations – held onto his by a landslide.

Of the baker’s dozen that the Citizens for Responsibility and Ethics in Washington reported being under investigation in its 2008 annual report, “Most Corrupt Members of Congress,” nine appear headed for re-election. (While Jefferson has a run-off in a month, the Times-Picayune calls him the hands-down favorite.) Of the four others in the baker’s dozen, three resigned. And just one lost.

Update: Here are the winners: