Put the strawberries, mint and honey in the bottom of a cocktail shaker or glass. Muddle well with the bottom of a wooden spoon.
Add the lime juice, vodka and ice. Shake well in a cocktail shaker.
Rub a piece of lime along the rim of the serving glass and dip in sugar.
Put 3 or 4 ice cubes in a glass and pour cocktail over it. If you were using a glass to mix, you will have to strain it. Top with club soda or seltzer.