I would say a hook, main character, a problem and some irony if you can.

I'd suggest that a logline's function is to be the hook ... so it needs to present a character with a problem. Either the character begins with a problem or is drawn into one (and we're generally interested in people's problems) and the problem should identify what the character's goal in the story might be. Then the action the character takes to deal with the problem. This action should suggest that the character's proposed solution is likely to lead to much deeper trouble. The suggestion that the action taken leads to deeper trouble can be stated as consequences of the action, which in turn suggest that there may be other forces of antagonism stacked against the character. So, Character in trouble acts to solve problems and causes greater troubles. Or, Character in trouble acts to solve problems and draws down the wrath of others. It seems to me that the description of the character has to offer up an alternative to stereotypes, and take action that might appear out of character, and face bigger troubles that, under normal circumstances, would be unusual.