The Doctor opened the door carefully, but he needn't have bothered. Jack wasn't asleep.
He was, however, well on the way there. He'd been reading, but he was looking extremely drowsy. He roused enough to raise any eyebrow at the Doctor, though, as he poked his head round the door.
"We're going out to find this Master's Doctor, because he knows where the evil one hangs out," the Doctor explained. "Will you be all right?"
"I'll be fine." Jack smiled, and wafted a hand towards the door. "Go. I'll let you fight my battles for me, for once."
"Thank you," the Doctor said softly, because he needed that. He crossed swiftly to the bedside and leaned over to kiss Jack firmly, then said lightly, "Go to sleep."
Then left, and hurried after the Master and Romana. He caught them up just as they entered the console room.