Comes news today that Police Chief Cathy L. Lanier has demoted Hilton Burton, commander of the force’s Special Operations Division, to a captain in the medical division. In other words, to police Siberia he goes.

Given that Burton quite publicly criticized Lanier over her handling of celebrity escorts, and given that Burton is party to a lawsuit accusing Lanier of racial and sex discrimination, this does not come as a total shock.

It is, however, yet another data point in a developing narrative of Lanier as a ruthless, arbitrary boss lording over the rank and file.

Just today, Examiner columnist Harry Jaffe claimed that officers are “demoralized as a result of the punitive discipline and the chaotic management style of Chief Cathy Lanier.” Washington Times reporter Jeffrey Anderson has published a series of articles questioning Lanier’s decisions to overturn the findings of police “trial boards,” imposing harsher sanctions than recommended.

Does any of this matter? No doubt Lanier is tough on her troops, but the polls show that by and large, that has not affected public opinion of Lanier and her department. A March poll by Clarus Research Group pegged her approval rating at better than 80 percent. The Post’s most recent polling found approval of the police department’s job at 76 percent — the highest level in more than 20 years of Post polling.

City Paper’s Rend Smith explored the issue in depth last month: Why is Lanier so darn popular — even though the officers union is constantly at war with her, she’s combative with reporters and she’s been embroiled in several controversies of varying magnitude?

What Smith concludes is that Lanier is a talented communicator and savvy navigator of the city’s various divides. I certainly concur with that, and I would add that Lanier quite cannily realizes that her job is not necessarily to please her officers, but to please the citizens her department serves. Lanier has kept crime under control and she has been responsive to community concerns. Internecine disciplinary squabbles, adverse arbitration rulings, nebulous claims of declining officer morale, the workaday power politics of a 4,500-employee bureaucracy have a negligible impact on the city’s perception of Lanier and her department.

In some cases, the harder on her officers Lanier is, the more the public appreciates it: The Washington Blade reported yesterday that Lanier told a gathering of gay activists, to some delight, that as many as seven officers could be disciplined, perhaps fired, after allegedly ignoring a hate-related attack. As much as Jaffe might paint “street cops” as a saintly caste oppressed by an out-of-touch command staff, a rigorous and fair disciplinary process is part of what makes a great police force.

The critiques certainly are that Lanier’s discipline is neither rigorous or fair (though I suspect the police union and general public might have differing standards). But as long as the public and the politicians that control her fate are satisfied, it seems Lanier will remain free to run her department however she likes.