You can avoid the tiny ice chips with a tea strainer, which you see at any respectable cocktail bar. You don't shake them because it over-dilutes and over-chill

You can avoid the tiny ice chips with a tea strainer, which you see at any respectable cocktail bar. You don't shake them because it over-dilutes and over-chills, as would stirring for 5 minutes. (It also oxygenates them and makes them a cloudy foamy mess, but that goes away on its own in under 5 minutes.)