Yesterday’s runoff in Mississippi was unique in many ways, but it did offer Republicans an instruction in the difficulty of “reaching out” to groups that are suspicious of them. Given the right circumstances, it’s possible for a Republican to successfully win over minority voters.

But Thad Cochran’s victory confirms two things about the difficulties of GOP minority outreach: everything has to be just right, and Republicans need something to offer beyond the hand of friendship. In other words, Republicans can’t just express a general desire to send a welcoming signal to minorities. It isn’t enough.

Cochran was able to get black Democrats to vote for him in the runoff not just because he showed up and shook their hands, but because he convinced them that their interests were aligned and if they joined him, they’d get something out of the deal.

To be clear, Cochran didn’t win solely because of black voters; his campaign also worked hard to turn out Republican supporters who hadn’t bothered to vote in the primary. But with a margin of less than 6,500 votes, it appears that he wouldn’t have won without those black Democrats. Cochran essentially ran two parallel campaigns, as this report from the Jackson Free Press described:

In a stepped-up ad campaign in Jackson publications, such as the Jackson Advocate and — in the interest of full disclosure — the Jackson Free Press, as well in mailings to majority-black Jackson neighborhoods, Cochran touts his support for historically black colleges and universities, the Jackson Medical Mall and Supplemental Nutritional Assistance Program, formerly called food stamps.

However, a campaign doorknob hanger Cochran campaigners left on homes in whiter Jackson neighborhoods such as Belhaven carried a very different message. It pictured all white men and emphasized Cochran’s support for the NRA and anti-abortion efforts, as well as the fact that he voted “more than 100 times” against Obamacare.

Cochran may not have been the African-American community’s best friend in Washington, but he had enough specific things he could point to in order to claim that it was in black voters’ interest to vote for him. And, importantly, he could plausibly argue that his opponent Chris McDaniel would do nothing for them, not only because of McDaniel’s extreme conservatism, but because the Tea Partier rejected the idea of using whatever power he could accumulate in Washington to serve Mississippi. If Cochran wanted a foil to convince black Democrats to join him, there would have been nothing better than a right-wing ideological crusader.

This confluence of circumstances demonstrates just how difficult Republicans’ task is when comes to reaching out to the groups among whom they perform poorly these days. If you start from a place of distrust, built up by a party that has demonstrated many times that it views them with hostility (as many Hispanics believe) or that it has outdated social values they find distasteful (as many young voters believe), then your pitch has to go beyond, “Really, we don’t hate you.”

But where can it go? Cochran could say, “I’m a hell of a lot better for you than Chris McDaniel” and hear black Mississippians respond, “I suppose that’s true.” But it will be much harder for a Republican candidate to make that case when the alternative is not an extreme Republican but a Democrat who is more likely to both share the values of the group in question and to have done concrete things for them in the past.

That isn’t to say Republicans shouldn’t keep trying to reach out, even if their efforts so far haven’t succeeded. They don’t have any other choice, if they want to be competitive in presidential elections and in purple states. But if they’re going to make any inroads at all, just reaching out isn’t enough. You have to have something real to offer people. And that’s the GOP’s real minority outreach challenge.