Messiah's Brook in Psalm 110

The LORD says to my Lord: "Sit at my right hand, until I make your enemies your footstool."...The Lord is at your right hand; he will shatter kings on the day of his wrath. He will execute judgment among the nations, filling them with corpses; he will shatter chiefs over the wide earth. He will drink from the brook by the way; therefore he will lift up his head.
Psalm 110:5-7

Yeshua confirmed that the Lord or Adonai spoken of in Psalm 110 is the Messiah, himself (Matthew 22:44), and the meaning of much of the Psalm is clear: shattering kings, judging nations, etc. But what does the final verse mean?

He will drink from the brook by the way; therefore he will lift up his head.

What brook is meant and why does it cause him to lift up his head?

It could refer to Yeshua's death and resurrection. In Genesis 40, Joseph interprets the dreams of two men and tells them both that Pharaoh will lift up their heads, one to be restored to service in the royal court, the other to be executed. "He will drink from the brook" could allude to Yeshua willingly accepting the cup of his fate (Matthew 26:39) and "he will lift up his head" could allude to the same thing again or to his subsequent resurrection and restoration to his place in Heaven.

However, this would break with the previous prediction of violent judgment that clearly must refer to Yeshua's return to judge the nation and set up his throne in Jerusalem. I won't say that it must be wrong--prophecy often ignores time scales and literal orders of events--but I think there is a much more plausible interpretation.

Consider these prophetic passages that discuss the same topics as Psalm 110:

And he will give rain for the seed with which you sow the ground...And on every lofty mountain and every high hill there will be brooks running with water, in the day of the great slaughter, when the towers fall. Moreover, the light of the moon will be as the light of the sun, and the light of the sun will be sevenfold, as the light of seven days, in the day when the LORD binds up the brokenness of his people, and heals the wounds inflicted by his blow. Behold, the name of the LORD comes from afar, burning with his anger, and in thick rising smoke; his lips are full of fury, and his tongue is like a devouring fire; his breath is like an overflowing stream that reaches up to the neck; to sift the nations with the sieve of destruction...Battling with brandished arm, he will fight with them. For a burning place has long been prepared; indeed, for the king it is made ready, its pyre made deep and wide, with fire and wood in abundance; the breath of the LORD, like a stream of sulfur, kindles it.
Isaiah 30:23-33 

Then he brought me back to the door of the temple, and behold, water was issuing from below the threshold of the temple toward the east (for the temple faced east)....Going on eastward with a measuring line in his hand, the man measured a thousand cubits, and then led me through the water, and it was ankle-deep....Again he measured a thousand, and it was a river that I could not pass through, for the water had risen. And he said to me, "This water flows toward the eastern region and goes down into the Arabah, and enters the [Dead Sea]; when the water flows into the sea, the water will become fresh. And wherever the river goes, every living creature that swarms will live, and there will be very many fish. For this water goes there, that the waters of the sea may become fresh; so everything will live where the river goes."
Ezekiel 47:1-9 

But let justice roll down like waters, and righteousness like an ever-flowing stream.
Amos 5:24

The gist of these prophecies is that when Messiah Son of David comes to set up his throne in Jerusalem, he will judge the nations with a thoroughness and violence not seen on earth since Noah. Rulers will be deposed, nations uprooted, and--most importantly--wickedness cleansed. The judgment of God is like a river that flows from the Temple, washing away the filth of oppression and sin, restoring life to the land as it goes. God's judgment even brings life to the Dead Sea, turning the saltiest body of water in the world into fresh water.

Psalm 110 describes Messiah's return in the end days as filling the nations with corpses, yet he pauses to drink from the brook along the way, and this drinking causes him to lift up his head. The brook referenced here isn't a metaphor of his own death. It is the overwhelming flood of God's wrath that brings relief to the land and to the righteous in Yeshua. He lifts up his head because he is refreshed and restored alongside his people whom he loves more than his own body.