The Case for the Koozie That Folds Flat
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Open the drawer where the picnic things live. There is a good chance it contains four or five rigid foam can coolers, each taking up the volume of a mug, none of them matching, most of them advertising a radio station or a wedding from 2018.
Rigid koozies have one flaw and it is a spatial one. Empty, they are still can-shaped. So they occupy the same space whether you are using them or not, which is why they end up in a drawer rather than in a bag, and why they are almost never with you at the moment a warm drink actually happens.
A sleeve that folds flat is the same object minus that problem. It lies down like a beer mat, slips into a side pocket, a glovebox, a picnic tote, or the gap in a bag where nothing else fits, and it comes out when a cold can does.

Ours is a plain white sleeve with a black interior, sized for a standard can and similarly proportioned bottles, in a soft collapsible wrap format. Plain is deliberate. The reason the drawer koozies are all branded is that people rarely buy their own, and a blank one does not date, does not advertise anything, and does not clash with whatever else is on the table.
What a sleeve does, honestly, is slow things down rather than chill anything. It insulates the can from the warmth of your hand and stops the condensation ending up on the table or running down your wrist. It will not make a warm drink cold. Nothing that weighs this little will.
Fit is by can, not by measurement: standard cans and bottles of roughly that size. Tall slim energy cans and wide craft cans are outside the shape it is cut for.
If the drink you are carrying is water rather than a can, the square bottle piece covers why the shape matters there too.