Dealing with blatant insubordination

[patrick03xx]

I have an employee who is publicly insubordinate to management. I have spoken with him about it privately, but it continues to happen in full view of others. From the reactions of those around him, no one takes it seriously. It does, however, need to stop. I am usually against public punishment as it can sometimes be taken as someone stroking their ego, especially by new hires to the company, but he's got me really close to making him a rare example to others. He has a ton of experience and adds value to the team, but I am worried that his behavior will cause an eventual erosion in discipline. What are some ways that you may have effectively dealt with this issue publicly but kept it balanced and fair?  

[mynewunit]

First question: Is he right?
Insubordination - not following orders. That is a little vague. It also takes some perspective. Jocko talked about this with Leif. Jocko wanted his guys to be following the uniform rules above and beyond the standards of the Teams so that it would help the relationship with the other branches. Leif and Delta Platoon commander went in direct opposition to Jocko's direction and had custom patches made for their team. They even had a radio call at the beginning of operations of "patches on".
What did Jocko do? Yell at them. Send someone home. Bust them down to 2nd Lt. No. He ignored it. It didn't ruin their operations. They felt like they some freedom. It never escalated or became a problem.
So what do you do with a helpful team member that doesn't follow rules, respect authority, or generally second guess the company brass. This takes an iron will and a light touch.
Option 1: He wants to be heard. This is a human element that could be the cause. He has something to say, good bad or otherwise. If you can get him a private audience with someone "in control" he can get it off his chest.
Option 2: He doesn't understand the mission. He might have some questions about the method or the process or blind spot to the "important" part of the job. This would be the time to double up on the meeting with the boss so they can clarify his role and how his work helps the project or company.
Option 3: He doesn't know he is doing something wrong. He might know that he is talking out of school but does he know how that is seen by you and others. If you have a deft manager who just listened to his comments to exhaustion and explained the mission,Clearly and consicely. He has set the table for him to then relay the behavior he is presenting for him to confirm, then explain why that behavior is not helpful, and what a productive version of that behavior would be, finally explain what the punishment would be for that behavior.
Make sure whoever does this practices it at least 3 times. Once where it goes great. Once where it goes horrible and once where it goes weird. None of the will be right but they might help establish guidelines for the interaction.
Good luck.
Remember the relationship is more important than the crime/punnishment/problem.