Place orange slices in a container of choice, preferably large, about half way filling the container.
Freeze water in containers, defrost slightly and dump contents into a stainless steel bowl.
Then split it up into 4 - 5 pieces with your least favorite knife, so each piece is a respectable size and place one on top the orange slices.
Measure out your Vodka. In the same measuring container, add both a gingerly dollop of Dirty martini olive juice, and some carbonated water so as to "pre mix" the Vodka and water. (I use a 3 oz pyrex measuring glass)
Pour into the drinking container.
Fill any void with more carbonated water.
I find the premix + the carbonation does a respectable job of mixing the ingredients. If it doesn't I don't care. (Hic!)
I have two of those water carbonating devices. My recipe is chill the water in the carbonating bottle very well; then add a teaspoon of baking soda. Then carbonate!
The colder the water, (not frozen) apparently adds more ability to assume carbonation. Also rock slightly after carbonation and while the carbonating bottle is still in the device. (all tested unscientifically of course).