The Doctor paced for a couple hours in their guest room that night. At last, River sat him down on the bed.

"What's wrong?"
"What's wrong! Nothing sits right with me about Loki's situation. I just do not know what to do. There must be some way to defeat this feeling of helplessness." He got up again, but she grabbed his arm, spinning him to face her.
"Rest. Come; the morning usually brings with it a new way to puzzle out a problem. We have at least that much time." River lay back against the feathered pillow which gave under her head. No matter. Both she and the pillow sprung up again in a minute.
"Oh, that reminds me. How long shall we stay here, my love? Oh my. Asgard already is growing on me. This would be a delightful place to live. People speak elegantly everywhere here."
"Yes, well, we shall stay about as long as it takes. There's something amiss here. Honestly, that's the best word for it."

The next morning, the Doctor's wife laid a hand on his arm to keep him from leaving the room right away.
"What's your plan?"

He smiled wryly. "I know I really shouldn't interfere with Loki's timeline, but it would be unjust for him to not know his whole life story."

She brushed her hair over her shoulders. "Are you going to tell him that he isn't from here?"

"No, unless I cannot help myself. Where might you be off to, my winding River?"
"Well, as we know, I am an archaeologist. I may as well act like it. After breakfast, I will ask for a tour of the palace and its treasures."
She sashayed to the door, where she spun on him, still standing in the midst of the room. "Second guessing your decision?"

"Ah, no. Not at all! Coming. We should exchange stories after our ventures."
He fiddled with his sleeve and the brace and darted after her.

In the dining hall, he found she was a few steps ahead of him in getting on with today's plan—she already had found a servant standing before the tables to ask for a tour. King Odin cocked his head, stepping behind her to hear her request.
The Doctor wore the same outfit and if his hair was more rumpled, who could tell? The sunlight made even the marble inside the palace gleam as though it was freshly laid. He left River to her conversations to try bacon and custard together. He survived.

After breakfast, he turned to leave, only to see the dark-haired, bright-eyed prince walk over to him.

Loki smiled. "Doctor, my friend, it is good to see you. I would like nothing more than to show you our finest means of traveling, though not mine to take out."
The Doctor beamed, eyes twinkling. "Yes. That's what the owner of the TARDIS said, before I appropriated her for myself. Be delighted."

Loki took the shortest path to the royal stables, still chuckling.
"I would like to hear more of how that came to pass. Ours was a typical day of keeping peace. A trader came to us from Vanaheim to offer a fine mare for his tribute. She had a silky coat, and the groom soon found out she was pregnant. Mother took a liking to her and practiced her magic to be sure the mare and her young were in optimum health.
"They were, yet when the colt was born, he made many a maid cry out with alarm, for he was a fine horse, but for one anomaly. He had double the legs. I wonder whom his sire might have been for raising such a sight. He's a dear horse, for now I am not the only one spoken of as strange.
"Here we are. Doctor, meet Sleipnir. Father had him trained and rides him everywhere. He is fleet of foot and very loyal. He never shies away from a battle, for it's in his blood."

"I see. That is amazing." The Doctor cleared his throat. "Ah, Loki, could I have a mome-?"

The prince in question ducked into the stall and began stroking Sleipnir's neck. He fed the horse an apple before looking up.

"Yes, Magician, is there some new topic you wish to discuss?"

He straightened his tie and coughed, waving his hand to dismiss the issue. "No. Not a new topic, but rather an old one. Have you…Ah, had a chance to speak with your fath—"

"Loki! I would speak with you!" Thor announced his presence as his voice loudly carried.

The Doctor jumped. He had been walking, trying to coax the words to fill the empty space his 'hemming and hawing' left behind, but backed up and bumped into nothing. No wooden wall, no beam, no one. Nothing visible, at least.

Thor ran his hand through his hair. "Loki!"

"I don't suppose you would believe that was not my fault?"

"No. I would not," Thor shot back.

River popped her head into the air and called out. "Sorry! That was me. I parked the TARDIS here silently. He always smacks into the wall when she's in invisibility mode."

"Yes, she's right; I do." The Doctor admitted. He spoke with River quietly, sticking his head halfway inside the TARDIS as he did so. She shook her head.

They withdrew just as Thor scrubbed at his hair and muttered an apology to Loki, who cocked his head to 'deliberate' before accepting the plea.

The blond prince soon chose to head to the sparring fields, muttering even louder about how much harder it was to tell if Loki was truly at fault for incidents, the comparative ease of routine defenses, etc.
Turning back to the Time Lord, Loki beamed at this revelation. "That is a clever bit of mischief! I wonder what the spell is for it."