What you could do, is first open up the mattress, note the order in which the foam is layered and then remove it (taking digital photos would help, plus you could post them here! I love to see mattress innards!

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Anyway, then take off all the foam as Sandman said, then lay on it and see if it feels like it's dipping in the middle, without the foam (you could leave the very bottom layer of whatever it is they have on there - god knows what it might be; could be some kind of burlap type stuff or a plastic-like material or a thin layer of foam. So anyway, lay on it and see if you feel the dip. If you do, game over, you lost: the springs are shot. (Unless it's a flippable mattress, then you can try the other side...)
If you don't feel a dip in the springs themselves, then you could try just removing the top most 2-3 pieces of foam and lay on that and see if it now feels a bit better.
Then if it feels like it's no longer dipping as much, buy yourself some latex. If it's a queen, buy queen sized latex, it'll fit. Any piece you might get that is too big can be easily cut to fit with an electric meat carving knife. Cuts like a hot knife through butter.
Now you're only question is how much foam do you really want? You won't probably need as many inches of foam as you had before, usually 2-4" will be enough. I use about 3", Sandman likes a little more.
Let us know how it turns out, and post photos if it's not too much hassle. Here's how to post photos:
How to insert pictures:
1. Select 'New Topic' or "Reply"
2. Enter text in the message area you wish to have surround the picture you are planning to add.
3. Select the 'Insert/Edit Image' icon just left of the smiley face, just above the message area. A small window pops up.
4. In this window type the URL of the image you wish to insert. It should begin with 'http://" and end with ".gif" or ".jpg". Where it says alternative text type a quick description of the photo. Click OK.
4b. If the picture is on your personal hard drive you will need to first upload it to a picture sharing/storage service like Flickr or imageshack.com. Once the picture is on that site you can simply cut and paste the URL of the image into the small window in step 4. On imageshack, after you've uploaded the picture, use the url next to where it says "Direct": copy and paste that url where it says url in the pop-up window here.
This message was modified Mar 12, 2010 by jimsocal