“Silvio” off of the much criticized Down in the Groove begins with couplet terminal rhymes:

“fast”/”past” and “got”/”not”. But then as soon as the bridge kicks in

Silvio
Silver and gold
Won’t buy back the beat of a heart grown cold
Silvio
I gotta go
Find out something only dead men know

with the monorhyme (aaaaaa), the rest of the song follows suit, with 5 verses of monorhyming lines before the bridge kicks in again at the end:

Honest as the next jade rolling that stone
When I come knocking don’t throw me no bone
I’m an old boll weevil looking for a home
If you don’t like it you can leave me alone

I can snap my fingers and require the rain
From a clear blue sky and turn it off again
I can stroke your body and relieve your pain
And charm the whistle off an evening train

I give what I got until I got no more
I take what I get until I even the score
You know I love you and furthermore
When it’s time to go you got an open door

I can tell you fancy, I can tell you plain
You give something up for everything you gain
Since every pleasure’s got an edge of pain
Pay for your ticket and don’t complain

One of these days and it won’t be long
Going down in the valley and sing my song
I will sing it loud and sing it strong
Let the echo decide if I was right or wrong

Silvio
Silver and gold
Won’t buy back the beat of a heart grown cold
Silvio
I gotta go
Find out something only dead men know

Plenty of perfect rhymes in this song for all perfectionists, “long”/”song” being one of them, and this is not a long song, rather short even, the stuff of catchy pop tunes, right there in every groove.
Here’s a live version from 1996 in Hyde Park with Eric Clapton, Ron Wood: