Well, okaaay...it's does sound weird, though.
At home I have made gimlets with vodka (Svedborg is great!) lime juice and a dash of splenda. Shake it up to make it frothy, and it's great.

Here's the text from the Low Carb Drink Menu that I designed for the Elm Street Bar in Dallas. The Syrups are all from DavinciGourmet.com. (I found a local supplier that sells me the syrups for about $6 US/750 ml.)

COCKTAILS (Under ½ gm net carbs)

LC Amaretto Sour
Vodka, Amaretto SF Syrup, Lemon-Lime Juice

LC Cinnamon Schnapps
Vodka, Cinnamon SF Syrup

LC Royal Watermelon
Crown Royal, Vodka, Watermelon SF Syrup, Lime Juice

LC Grape Shot
Vodka, Grape SF Syrup, Lime Juice

LC Cherry Limeade
Vodka, Lime Juice, Cherry SF Syrup, Soda

LC Hawaiian Sunset
Vodka, Pineapple SF Syrup, Lime Juice, Dash Cherry

LC Fuzzy Navel
Vodka, Peach SF Syrup, Orange SF Syrup

LC Margarita
Tequila, Lime Juice, Orange SF Syrup

LC Peach Margarita
Tequila, Lime Juice, Peach SF Syrup

LC Piña Rita
Tequila, Lime Juice, Pineapple SF Syrup

LC Piña Colada
Rum, Pineapple SF Syrup, Coconut SF Syrup, Cream

LC Kahlua & Cream
Vodka, Kahulí Caffé™ SF Syrup, Cream

LC Hazelnut Cream
Vodka, Hazelnut SF Syrup, Cream

LC B-52
Vodka, B-52 SF Syrup (Kahlua, Bailey’s, Grand Marnier), Cream

SF JELLO SHOTS
Vodka, SF JELLO (various flavors)

SF Red Bull Cocktail
Vodka, SF Red Bull. 1.5 gm net carbs


BEER

Michelob Ultra (2.6 gm net carbs)

Rock Green Light (2.6 gm net carbs)

Miller Lite (3.2 gm net carbs)

Coors Light (4.4 gm net carbs)

Amstel Light (5.0 gm net carbs)

Bud Lite (6.6 gm net carbs)

Thank you, gotbeer! I'm going to print that drink list out right now.

Generally I'm quite happy with gin & diet tonic, but this opens up a world of possibilities.