Okay, this one is seriously wonderful -- none of that Banana Splits, I'm-being-partly-ironic crap.
From 1972, here's the great Brinsley Schwarz and their instantly addictive "Unknown Number." Written and sung by the pre-irony Nick Lowe on their ace Silver Pistol album.
The reason it sounds a little roughhewn is that it was recorded, as you may be able to glean from the album cover, at home. The Brinsleys (with new 2nd guitarist Ian Gomm) had retreated to a communal house (inspired by you know who) to lick their wounds after their first two studio albums bombed in the midst of one of the most disastrous live hypes in rock history (the details are here). Their plan: Move a mobile 24-track recording machine into their living room and try to make music on a slightly more intimate scale.
It worked, as you can hear from this song, although it didn't translate into record sales. In any case, this is Lowe chanelling Buddy Holly's "Words of Love," I think, and it's just hauntingly lovely.