Yes, jmh, there is nothing so serendipitous as searching for a word and finding a whole new world!

Brewer has: The Scots call a cloven hoof a 'cloot', so that Auld Cootie is old Clovenfoot

and follows with this citation (pardon my accent):

And maybe Tam, for a' my cants,
My wicked rhymes an' drunken rants
I'll gie auld Cloven Clootie's haunts
An unco slip yet,
An' snugly sit amang the saunts
At Davie's hip yet!

Burns: Reply to a Trimming Epistle.

-- and the unusual scanning of the latter half reminded me immediately of Ogden Nash's verse about a husband:

He tells you when you've got on too much lipstick,
And helps you with your girdle when your hips stick.

Little devil, isn't he!