I don't know the answer on this but I was just lamenting the same problem yesterday at our weekend lake place. We have regular mattresses too and I just bought new sheets that have about twice as much fabric as I need. I thought if I bought relatively inexpensive sheets they would have skimped on the fabric but not a chance.

I love my old, old sheets. They weren't expensive, they're soft, don't wrinkle, don't pill and don't have excessive fabric. Unfortunately some have just worn out.

Hope someone has an answer on this.

Thanks nanny, I just checked out the sheets from Vermont Country Store. They look very nice. Do you find that they need ironing? Some cotton sheets seem to come out of the dryer looking so rumpled that even though I HATE to iron I find myself having to at least touch them up a bit. Others seem to do just fine, and I haven't figured out why.

I found some Laura Ashley sheets on Overstock that have a 12" pocket, and I have ordered them. I have a few beds that need these shallower sheets so I'll probably be checking out several. I'll be interested to hear how the Vermont Country Store sheets come out of the dryer.

Thanks!

Ikea sells thinner mattresses and sheets to fit, ranging from $25-35. Looks like the sheets are just available in-store, though, and I haven't personally tried them to know how they wear.

Thank you for your interest in Vermont Country Store's Shallow Depth Sheets. I wanted to let you know (from experience) that these sheets come out of the dryer nice and crisp. I have owned them for a little over a year and you wouldn't be able to tell that they had been used . I have never needed to iron them, just wash and dry, and remake the bed. Plus we have a 100% satisfaction guaranteed forever on all of our products. If you have any questions or concerns, please don't hesitate to contact us at 1-800-564-4623. Thank you, Vermont Country Store Customer Service.

Walmart's jersey sheet sets are perfect for cottage size beds, I have them on all the beds in the lake house. They're comfy like a tee shirt and easy peasey to maintain and only $25.00 a set. The hug the mattress beautifully, ours are 10 inches also. They last for years.

I will back up what Michelle said. I just put mine in the wash and dryer for the first time, and they came out great, crisp and ready to put back on the bed. Even the header at the top was unwrinkled - a pet peeve of mine because all my other sheets have wrinkled headers that I always have to iron to look good on the bed. I sleep "hot", so these sheets have been much more comfortable for me at night, they stay cool and do not get all clammy feeling like my other sheets do. I am so glad that I found these!

Unfortunately, those lovely wrinkle-free sheets probably contain formaldehyde. http://saferchemicals.org/2013/07/12/ill-keep-my-wrinkles-thanks/

We found some here that are very nice - not high end tailored (no border at the top of the fitted sheet, for example), but nice jersey material.

http://www.amazon.com/Textiles-Plus-Cotton-Jersey-Sheet/dp/B00YEABJVG?ie=UTF8&psc=1&redirect=true&ref_=oh_aui_search_detailpage

I could not find the shallow depth fitted sheets on Vermont Country Store's website, but they can be ordered from Pioneer Linens in West Palm Beach FL. I have a Charleston Rice bed and have to have my mattress custom made to an 8-9 inch depth or I'd lose the headboard and have to get a ladder to climb in bed! A pox on the makers of these ridiculously thick mattresses!

I have a sleep number type air bed with 9" mattress it is not special made and I love it. You might try that when you need a new mattress

I just found that if I order sheets for a sofa-bed they will fit my 5-6" mattress in my Little Guy 5 Wide camper/trailer.

Good luck finding a shallow pocket sheet. I have been looking FOREVER!

Part of the problem is that people assume that their mattress is the standard, advertised size. Like an standard King is supposed to be 76x80 but MANY manufacturers cut their mattresses short, believe it or not. Tempurpedic is notorious for cutting their mattresses short (Saves them money? Who knows.) The point is - the pocket depth being wrong is not the only problem you will have with getting a tight fit and avoiding swimming in bunched-up sheets on your bed.
We have a Tempurpedic King mattress that is actually 74.5 inches wide by 79 inches long and 11.5 inches high.
The thing to do is to order from custom sheet companies. These sheets are not that much more expensive than many premade sheets and often are higher quality. We ordered fitted sheets to match our existing sheet sets (similar colors) and the prices were quite reasonable.
Good companies we found include CozyTown (https://cozytownlinens.com/ Call or read instructions on how to order custom sheets - they want you to choose the general size in the dropdown list then in the comments section tell them the actual mattress measurements). They use only long staple cotton. Their Italian and 300 thread count sheets are really nice and ship fast, while their 500 TC takes a bit longer to order.
CustomMattressFactory.com is another company with 600 TC organic cotton that is even less expensive than the former company.
But there are a lot of companies doing this sort of customization. We gave up searching for premade sheets to fit the beds and have finally gotten sheets that fit.