My living situation is changing and I need to hide my porn collection.

The smallest rentable space I can find is a 5x5 storage unit--much bigger than what I needed and a waste of money.

I'm fine with throwing out the DVD cases sent just keeping the discs until I get them digitized. So I'd only take need a small locker, enough to hold a large CD/DVD case.

Any suggestions where I can rent space like this?

(I know this isn't escort related, but I figured it was sex related and didn't know where else to ask. Thanks!)

Check with you bank on how much it is to open a safe deposit box.  

bus and train stations used to have lockers where, for 50 cents, you can lock up an item for weeks on end.  

See if any of these near you still have them.

 
If hiding it from your wife, just put them in the oven.

Use a bank safe deposit box.  The annual fee for one is very reasonable.

Yes, I think that transit station lockers are history ... for security reasons. But even back then, most lockers were PER 24 HOURS. The lockers were monitored. If not opened and the contents reclaimed within 24 hrs, it was removed as abandoned property. You would have to visit the lockers every day, 7 days / week.  Large terminals had a big baggage storage room, where you could drop off bags / boxes with the humans working there and get a claim ticket good for more than 24 hrs.  
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A post office box might be cheaper than a safe deposit box. Some look like a big drawer. Or, you could mail the package to yourself and make it look like it's something work related that you have to forward to someone else or hold until they arrive at your location, so you can't open it.  
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Some shipping / storage / warehousing companies are flexible on what they will store and for how long. Years ago, I had a fragile item shipped to me (via a small shipping company, not USPS, UPS, FedEx, ...). They stored it at their warehouse until I was ready to pick it up and use it, for around 3 months. When I went there to pick it up, it was a box on a shelf in a wide open area with lots of other boxes, and the shipping tags and warehouse location sticker / shelf tags on the box. Not as secure as a bank, but I wasn't shipping diamonds or gold bullion. Oh ... if you just need warehousing, you don't have to ship it, just bring it to the warehouse, let them tag it and store it.

Good one.