This is a question for all the ladies of StackExchange.
As a frequent traveller, I've found a few ways to pack bras better but I wanted to reach out to the peanut gallery and see if there was any other way to pack these things any more efficiently.
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Whenever the topic of packing something in an optimal way comes up, it's useful to see if the Navy has anything to say about it. The Navy is a good place to look because sailors need to be especially diligent about packing economically, and women sailors are no exception.
Specifically, women in the US Navy are issued 11 bras and should have 2 in their seabag ready for deployment. The rest should be stored in their locker at port. These are of the type: sports, white or beige. Your question did not specify a given bra type, so this answer would apply to sports bras rather than the cantilevered or balconette or contoured or other bra types.
Pursuing this topic, it turns out that the US Naval Academy provides female midshipmen with instructions on folding their bras...
b. Brassieres. Divide into thirds; fold right third and then left third back; fold top straps down to form a square; stack in locker with bottom sweatbands flush and facing out (Figure 6-B).
...and to help get the point across, they provide an image...
Source: Midshipmen Uniform Regulations
Presumably the required square shape is the result of computing optimized surface area versus volume.
They make a point of explaining how the bras should be stored in the locker, but it's implied that storage for deployment would follow the same pattern. It's a good bet that the Navy hired external contractors to study the problem and produce a report which then informed the regulations.
Nobody likes a tired, frumpy bra that's been crushed in a suitcase, and if you eschew the sports bra in favour of the cupped bra style, then consider some of the recent innovations in specialist luggage.
Pad it with socks and underwear. (default strategy)
Pack them near the top. (not sure how helpful this really is in actual execution since you can't control baggage handling after check-in...)
Stack them. (strength in numbers! my go-to move.)
Fold one cup inside another. (I see this everywhere in FlyerTalk forums but according to experts, this actually stretches the bra out??)
Use a special case. (this seems excessive but I could see how a packing-cube-like system would help)
I know this is more of an opinion-based question but has anyone out there actually found an objectively best way to pack bras on a trip? Let me know! :)
This may work for some type of fancy lingerie
Some other tips:
Probably if you travel a lot it'll be better to have a hard case for those purposes