Ask for no lid when you are drinking straight away, and no straw or stirrer. The lid is the single heaviest piece of plastic on a takeaway drink.
Life-cycle studies of takeaway coffee cups use a polystyrene lid of about 3 g (3.2 g in a study for the reusable-cup company CupClub, and 3 g assumed in one for KeepCup). One drink a working day adds up to roughly 750 g of plastic a year. Combined with a reusable cup it closes the loop entirely.
The catch: hot drinks without lids spill; this is a swap for when you are drinking at the counter or walking a short distance.