Rio Bravo

In the movie, ‘Rio Bravo’, with John Wayne, there is a song by Dean Martin & Ricky Nelson, what is it’s name?

I have never been able to ID the name of that song. One refrain goes through my mind is “With my 3, good companions, my rifle, my pony and me”

“My Rifle, My Pony, and Me”
Music and Lyrics by Dimitri Tiomkin and Paul Francis Webster
Performed by Dean Martin and Ricky Nelson

The sun is sinkin’ in the west
The cattle go down to the stream
The redwing settles in her nest
It’s time for a cowboy to dream

Purple light in the canyon
That’s where I long to be
With my three good companions
Just my rifle, pony, and me

Gonna hang my sombrero
On the limb of a tree
Comin’ home sweetheart darlin’
Just my rifle, pony and me

(Whippoorwill in the willow
Sings a sweet melody)
Ridin’ to (Ridin’ to) Amarillo (Amarillo)
Just my rifle, pony, and me
No more cows (no more cows) to be ropin’ (to be ropin’)
No more (strain)STRAYS will I see
Round the bend (round the bend) she’ll be waitin’ (she’ll be waitin’)
For my rifle, pony, and me
For my rifle, my pony, and me

My Rifle, My Pony and Me – Dean Martin and Ricky Nelson