"Captain, I respectfully request that you cease flirting with me while we are on duty."
"Why? And didn't I tell you to call me Jim when we're off-duty?"
"Yes, Jim. Such behavior encourages idle speculation among the crew regarding the nature of our relationship."
"Spock, it's called gossip. You know as well as I do that the rumor mill is a fact of shipboard life. Has anyone said anything to you?"
"Negative. I simply believe it would be prudent to avoid "adding fuel to the fire", as you would say, by being more discreet in our public interactions."
"Well, I haven't heard anything. If nobody has said anything to you or me about it and neither of us has overheard anything, I think we're doing a pretty good job of being discreet. Don't you think that my not flirting with you would be grounds for more speculation? I flirt with everyone, Spock. Nobody cares. Most of the time it doesn't even mean anything. You don't want the crew to think we're fighting, do you? Because that's EXACTLY what they'll think if I suddenly change my behavior towards you, and nothing sinks morale faster than rumors of conflict at the command level. We have a happy ship. Let's keep it that way."
"You are correct, Jim. Any significant alteration in your established behavioral patterns would draw more attention than continuing as you have been. My apologies. I merely find the idea of our relationship being the subject of speculative rumor to be... disquieting."
"No problem. I know how much you value privacy. And since we're safe behind closed doors, let me draw your attention to another established behavior pattern of mine, Mr. Spock..."
Jim's concerns about a happy crew aside, Spock knew it was even more important to keep one's mate happy - especially when said mate is a human starship captain.