A private conversation is one that only you and one other person can see. Private conversations are called "queries" in Konversation. To initiate a private conversation, type /query nick in any input line, where nick is the nickname of the person you want to talk with. You can also click with the right mouse button on the person's nickname in the Nick Panel and choose Open Query. A new tab will be created. Announce yourself by sending a message.

Queries are just like channels, except that only you and the other person can participate in the channel.

To leave the query, just close the tab. Note however, that if the other person sends you another message in the query, the tab will open again.

To leave all queries, choose Window → Close All Open Queries on the main menu, or press F11 key.

When someone else initiates a query with you, Konversation creates a new tab with their nickname. If you don't wish to talk with the person, close the tab.