Double straining removes ice shards, fruit pulp, and herb fragments from anything served 'up' (no ice). Hold the Hawthorne strainer over the shaker tin and a fine-mesh tea strainer between the shaker and the glass. Pour through both. Any cocktail served in a coupe, Nick & Nora, or martini glass must be double-strained. Drinks served over fresh ice (rocks glass with a fresh cube) only need single-straining — the new ice covers any debris.