Soon after Grettir had left the Arnarvatn Heath there came a man there named Grim, the son of a widow at Kropp. He had killed the son of Eid of Ass, the son of Skeggi, and been outlawed for it. So there he stayed where Grettir had been before him and got plenty of fish out of the lake. Hallmund was not at all pleased at Grim being there instead of Grettir, and said that he should have little advantage from his great catches of fish. One morning Grim had caught a hundred fish, which he brought to the hut and arranged outside. The next morning when he went there every fish was gone. He thought it very strange, but returned to the lake and caught this time two hundred. He carried them home and arranged them; again everything happened as before; in the morning all were gone, evidently through the same agency as before. The third day he caught three hundred, carried them home and kept a watch on his hut. He looked out through a hole in the door to see if any one came, and so he remained for a time. When about one third of the night had passed he heard some one walking near and stepping rather heavily; so he immediately took his axe, which was very sharp, and wanted to know what was the matter. There came a man with a big basket on his back; he put it down and looked round, but saw no one outside. He rummaged about among the fish and seemed to think that they would do for him to lay hands upon. He threw them all into his basket and they quite filled it. The fishes were so large that Grim thought no horse would be able to carry more. This man then took the load and got beneath it. Just as he was about to rise Grim rushed out and taking his axe in both hands struck a blow at his neck which went through the skin. He started in surprise and then ran off towards the south of the hill with his basket. Grim went after him to see whether he had got him. They went south along the foot of the Balljokull where the man entered a cave. There was a bright fire in the cave and a woman standing in it, very tall but shapely. Grim heard her greet her father, calling him Hallmund. He flung down his load and heaved a great sigh. She asked why he was covered with blood. He answered in a verse:

Then she pressed him to say what had happened, and he told her everything.

"Hear now," he said, "what I tell you of my adventure. I will tell it to you in verse, and you shall cut it in runes on a staff."

She did so, and he spoke the Hallmundarkvida, in which the following occurs:

Many exploits of his did Hallmund recount in the lay, for he had been in every land.

The daughter said: "That man was not going to let his catch slip away from him. It was only to be expected, for you treated him very badly. But who is going to avenge you?"

"It is not certain that anybody will, but I think that Grettir would avenge me if he were able. It will not be easy to go against this man's luck; he is destined to great things." Then as the lay continued his strength began to fail. Hallmund died almost at the moment when he finished the song. She grieved much for him and wept sorely. Then Grim came forward and bade her be comforted. "All," he said, "must depart when their fate calls. It was partly his own fault, for I could not look on and see myself robbed."

She said he might speak much about that: "The unjust man prospers ill."

She was somewhat cheered by the talk with him. Grim stayed several nights in the cave and learned the lay; all went well with them. Grim was in the Arnarvatn Heath all the winter after Hallmund's death. Afterwards Thorkell the son of Eyjolf came to the heath and fought with him. The meeting ended by Grim having Thorkell's life in his power, but he would not kill him. Thorkell then took him in, sent him abroad and supplied him with means; each was considered to have acted generously towards the other. Grim became a great traveller and there is a long saga about him.