There's a difference between travesties (for which you really need to know the base song) and genuine short ballads which stand alone. Here's my favorite:

I Was Standing On the Corner         (From Ed McCurdy)

I was standing on the corner
Just as lonely as could be,
When up there came an ugly man
And tied his horse to me.
---

Actually, I've been collecting these for some while. Here's a few others:

Bessie Bell and Mary Grey         (Child #201)

Bessie Bell and Mary Grey,
They were twa bonnie lasses.
They biggit their bower on yon burnside
And thackit ower wi' rushes.

They thackit ower wi' rushes green,
They thackit ower wi' heather;
But the plague cam' fae the borrow toon
An' burried them baith thegaither
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The Colorado Trail

Eyes like the morning star,
Cheeks like the rose,
Laura was a pretty girl,
Everybody knows.

Weep all ye little rains,
Wail winds wail,
All along, along, along,
The Colorado Trail.

----------------------

Dog Tick         (from Peggy Seeger)

Dog tick, dog tick, dog tick, 'bacco worm,
Why can't a dog tick dance like a 'bacco worm?

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The Lady in Red         (From Dr. IS Posen)

See the lady in red,
Makes her living on her bed.
For fifteen cents she'll do it once;
For twenty-five cents she'll do it twice.

Here I stand
With a nickel in my hand...
Hey buddy, can you spare a dime.

(Legman notes that the 15 cent price is part of the joke as it's ludicrously low. Typical depression-era low-cost cost was about $2, rising to $5 with the War. He suggests that the song may include the hidden admonition "that the reward of sin may not always necessarily be death, but it ain't much."

-----------------------------

Bob-Tailed Mare       As sung by Phil & Sid Taylor (Sifalid) of near Edinburgh

Of all the horses in the merry green wood
The bob-tailed mare bears the bells away.
There is "Hey," there is "Ree," there is "Whoa" there is "Gee,"
But the bob-tailed mare bears the bells away.
"Hey, Ree, Whoa, Gee,"
But the bob-tailed mare bears the bells away.

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There's many more verses but I think probably 99% of the times its actually sung, "Cottoneye Joe" is simply:

Where did you come from? where did you go?
Where did you come from, Cottoneye Joe?

I come for to see you, come for to sing,
Come for to show you my diamond ring.

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The 1930'S                     (by Bob Davenport)

The 1930's was always on my mind,
So a steady job was the thing to find.
Now as Wall Street totters and a slump grows near,
Thank the Lord,
I've got a barber's job...in a maternity ward.

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Ye Can't Put Yer Muck in Oor Dustbin         (Glasgow street song)

Ye can't put yer muck in oor dustbin
   Oor dustbin, oor dustbin.
Ye can't put yer muck in oor dustbin
   Oor dustbin, fu'

---------------------------------

WAD YE DO THAT?         (Robert Burns, in _Merry Muses of Caledonia_, page 14   
         Tune: John Anderson, my jo)
                           
Gudewife when your gudeman's frae hame,       [away from]
   Micht I but be sae bauld,
As come to your bed-chamber,
   When winter nichts are cauld;
As come to your bedchamber,
   When nichts are cauld and wat;
And lie in your gudeman's stead;
   Wad ye do that?

Young man an ye should be so kind,
   When our gudeman's frae hame,
As come to my bed-chamber,
   Where I am laid my lane;                   [alone]
And lie in our gudeman's stead,
   I will tell ye what,
He f---s me five times ilka nicht,            [fucks, every]
   Wad ye do that?

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Supper Is Na Ready         (Robert Burns, in _Merry Muses of Caledonia_, page 45, Tune: Clout the Cauldron - as they all are- learned from MacColl. That is, I did. I don't know where Burns got it.)

Roseberry to his lady says,
        "My hinnie and my succour.
"O shall we do the thing you ken,
        "Or shall we take our supper."
                        Fal lal &c.    [MacColl didn't sing "Fal lal &c."]

Wi' modest face, sae fu' o' grace,
        Replied the bonny lady;
"My noble lord do as ye please,
        "But supper is na ready."
                        Fal lal &c.

----------------------------

My Brither Bill         (Glasgow street song, per MacColl)

My brither Bill's a fireman bold,
   He pits oot fires.
Only twenty-three years old,
   He pits oot fires.
He went to a fire the other night
When somebody shouted, "Dynamite!"
Wherever he is, he'll be all right.
   He pits oot fires.

----------------------------

My Ma's a Millionaire        (Glasgow street song, per MacColl)

My ma's a millionaire,
Big feet and curley hair,
Walking down Buchannan Street
With her big banana feet
My ma's a millionaire.

------------------------------

"Old Aunt Kate"        (From Peggy Seeger)

Old Aunt Kate she baked a cake
She baked it 'hind the gar-den gate.

She sift the meal and gimme the dust,
She baked the bread and gimme the crust,

She eat the meal and gimme the skin,"
And that's the way she took me in.

-----------------------------------

Old Mother Riley        (learned from Phil & Sid Taylor &
                         in _101_ Scottish Songs)

Old Mother Riley at the pawnshop door,
Baby in her arms and a bundle on the floor.
She asked for ten bob, she only got four,
And she nearly pull't the hinges off the pawnshop door.

------------------------------------

Oor Cat's Deid        (learned from Phil & Sid Taylor &
                         in _101_ Scottish Songs)

Lingle lingle lang tang oor cat's deid
Whit did she dee wi'?
Wi' a sair heid!
A' ye that kent her
When she was alive
Come to her funeral
Atween four and five.

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Siembamba          (a S. African mother's song, per Marais & Miranda)

Siembamba, momie's baby,
Siembamba, momie's baby,
Twist his neck and hit him on his head,
Throw him in the ditch and he'll be dead.

Siembamba, momie's baby,
Siembamba, momie's baby,
Just for love she throws him in the ditch,
Momie's sweet little, sweet little.........baby.
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Some years back, Paul Stamler began to count words, seeking Shortest Stand-alone ballad. He offered the above-mentioned, "Papa loved mama" as being only 14 words.