The Carter recording (transcribed 6/17/2013) is a duet with Walter Jacobs. Jacobs is immediately recognizable as the vocalist from the Mississippi Sheiks. His correct name appears to be Walter Vinson, but he's also given as Vincson and Vincent on various disk labels.

I'll chip in two pretty good hillbilly versions, both individualized enough to rise above mere "cover" status.

RED'S TIGHT LIKE THAT
Tune Wranglers, San Antonio, 2/27/1936, Bluebird B-6438, lead vocal and tenor banjo by "Red Brown" (Joe Barnes), addl vcl chorus by the band in parentheses, call-response. Instrumental solos from fiddle, tenor banjo, and piano

Now I had a girl and her name was Kate
She could shake it so well, she shake like jelly on a plate
Oh, it's tight like that (tight like that), it's tight like that (tight like that)
Can't you hear me talking to you, I said it's tight like that (it's tight like that).

She could shake it so well, she laid it on the shelf
Said if you want any more, you've got to shake it yourself

Now she wouldn't and she couldn't and she didn't come at all
She pulled up her stocking and leaned against the wall

Now, apples on the table, peaches on the shelf
I'm gettin' mighty tired of sleepin' by myself

I'm not the butcher but the butcher's son
I can cut your meat until the butcher comes

Now I don't know but I've been told
That the ladies in heaven like to sweet jelly roll


TIGHT LIKE THAT
Otis Mote, hca/gtr/vcl, Richmond, VA, 10/17/1929, released on OK 45389. Mote has an almost alto voice and plays harmonica very much like Gwen Foster, taking several breaks between verses. Lyrics are similar but not identical to the first recording by Tampa Red and Georgia Tom, and he doesn't "beedle-um" in the chorus (though he scats a verse in beedle-ums).

Uncle Jack oome home 'bout half past ten
Put the key in the hole but he couldn't get it in,
It's tight like that, Lord, lord, it's tight like that
Don't 'ee hear me talkin' to you, honey, it's tight like that.

Little red rooster said [to] the little red hen
[?Make a date] at the gate 'bout half past ten.

Little brown rooster said (to) the little brown hen
You ain't laid an egg since Lord knows when

Little brown hen said [to] the little red rooster
You don't come to see me just as reg'lar as you use-ter

My ma had a dog, she named him Ball
Give him a little taste and he wanted it all

Went to see my gal, across the hall
Had another mule kickin' in her stall

If you see my gal, hurry home
Ain't had no rest since she been gone

Mote also scats a verse with variations of "beedle-um-bum," between the last two harmonica solos.