According to John Dittmer in his book Local People: The Struggle For Civil Rights In Mississippi, affluent, powerful white segregationists wanted to keep the Klan down because they thought its violent tactics would hurt their fight against civil rights.
Dittmer singled out the Yazoo Citizens' Council by name:
The Yazoo City chapter of the Citizens' Council went on record opposing the Klan, adding that "your Citizens' Council was formed to preserve separation of the races, and believes that it can best serve the county where it is the only organization operating in this field."
They followed other prominent Mississippians who were trying to quash a resurgence of the Klan in the wake of the civil rights movement. Sen. John Stennis (D-MS), Dittmer wrote, condemned the Klan thusly:
Senator John Stennis, while not mentioning the Klan by name, condemned the rash of cross burnings, warning that such actions "can only hurt us in our efforts to defeat the [civil rights] bill because it gives our opponents an additional weapon to use against us."
"The Klan was bad for public relations," Todd Moye, an associate professor of history at the University of North Texas and the author of Let the People Decide: Black Freedom and White Resistance Movements in Sunflower County, Mississippi, 1945-1986, tells TPM.
Citizens' Councils "were trying to bring business into the state, and you know the Northerners with capital aren't gonna build factories in the state if they think it's a bunch of yahoos burning crosses," Moye said. "But if these people can maintain the status quo, which was based on Jim Crow segregation -- if they can do that without resorting to those bad publicity stunts -- then that's what they want to do. It's a white supremacist group, there's no question about it."
They weren't entirely successful at eradicating the Klan, regardless of their efforts. As Justin Elliott at Salon notes, reports from the time refer to members of the "Yazoo City Kavern," the name for a local Klan organization.
(Eric Kleefeld contributed reporting to this story.)
[Ed. note: This post has been edited since it was first published.]