Japanese actually has a few different phrases for 'plastic bag'. All of them are variations on the word fukuro (袋), which means 'bag' in Japanese. (When you add other words in front of it, the 'f' sound changes to a 'b').
A reji bukuro (レジ袋）is the best word for one of those plastic bags you get at the register (reji is actually short for the English word 'register').
You also might hear bineeru bukuro (ビニール袋). This is again a weird English loan word, which comes from a mispronunciation of the English word 'vinyl'. You might hear cashiers asking you if you'd like a bineeru bukuro (plastic bag) or kami bukuro (paper bag).
Finally, if you've managed to dissuade the bakery attendant from putting each of your pastries in its own bag, but they'd still like to put them in one big bag with a handle, you'll want the phrase sage bukuro (提げ袋) which means 'bag with a handle'.
To politely decline any of these bags, just insert your bag phrase of choice and finish with 'wa iranai desu'.
For example, 'reji bukuro wa iranai desu.' ('I don't need a plastic bag.')
For an easier catch-all, try the phrase 'sono mama de daijoubu desu,' which means 'Just that is okay'. (At a pinch, 'sono mama' works just as well.) Say this when your cashier reaches for a bag and they'll know that you mean sans plastic bag.
Though plastic bags are definitely the most glaring example of over-the-top plastic love, there are other types of plastic you might encounter that you can also try to refuse.
Ever wonder what those little green stoppers they sometimes put in your cup at Starbucks are called? Madorā (マドラー), with an emphasis on the last syllable. This one also has a funny English loan story. It technically means 'stirrer' (though it's what the baristas call the green stoppers too) and it comes from the English word 'muddler', meaning that tool that bartenders use to muddle ingredients.
Try this one out at your next Starbucks trip: 'Madorā wa iranai desu.' ('I don't need a little green stopper.')
And if you can go without a plastic lid (futa, 蓋) or a straw (sutorō, ストロー, like the English word) try to turn those down too.
A lot of cafés and bakeries in Japan will offer mugs and glasses instead of plastic if you dine in. Another great way to cut down on your plastic use is just to avoid doing take-away as much as possible.
To tell your cashier you plan to dine in, say 'Tennai desu.' (店内です). And to specifically request a mug over a plastic to-go cup, try 'Magu capu wo onegai shimasu.' (マグカップをお願いします).
Or, if you're on the go, maybe try bringing your own travel mug. A lot of cafés will even give you a discount for using your own container. Just show them your travel mug and say, 'koko ni irete kudasai' (please put it in here) or 'tambura ni irete kudasai' (please put it in my tumbler/travel mug).
Guide to Japanese etiquette
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