Sloppy Joe's SpecialI have no idea where the name of the drink originated. My source is a handy little cocktail app for my iPod touch that has collected dozens of drinks from various sources. This one was published in "The Gentleman's Companion: Being an Exotic Drinking Book, or Around the World with Jigger, Beaker and Flask" published in 1946. I won't link to it on Amazon because pretty much the only copies available are used and approaching $200.
1 oz good gold rum (I used Bacardi 8, but if you have some Cuban rum secreted away that fell off a truck, use that)
1 oz dry vermouth (Noilly Prat & Cie is my brand)
juice of 1 lime
2 bar spoons grenadine
2 bar spoons curaçao (I swapped in triple sec)
Stir all with cracked ice and strain into a cocktail glass.
In terms of flavor, the lime juice really tends to overwhelm this, and I didn't use much, only about 3/4 oz. I'd scale it down to 1/2 oz lime juice, just so you can taste the rum a bit more. Other than that, it's sort of a modified Sidecar with rum and vermouth. There's some subtleties there, but until you get rid of some of the lime, you'll never taste them.
EDITED on 8/1/09 to add: I've got a lead on where the name comes from...apparently in Prohibition-era Cuba, there was a bar called Sloppy Joe's. More info can be found here.