Longshot ID  

They sure look high end.
They sure look high end.

I've seen these mostly attributed to Gio Ponti.

Superb
They are superb. I have never seen them atttribuited to Gio Ponti, however I have seen them attribuited to Ico and Luisa Parisi. Regardless, an attribuition is just an attribution. Until there is a real authority to point towards a name they will remain just attributions. They are both beautiful pieces. Enjoy them, whether you keep or sell them. Good luck in findind out the real name behind these!

Thanks for the help.
Based on both your suggestions, I did some research. I couldn't find any tables like mine by Gio Ponti. Doesn't mean they aren't by him, just that I couldn't find them. But I found a very similar one by Ico and Luisa Parisi (see pic below) and Luisa was a student of Gio Ponti (maybe that's significant, maybe not). My table and the Parisi one are so close in style that the coincidence is almost too great to be a coincidence. Do you think mine could be another Parisi iteration, or perhaps a very good knock-off?

The feet on my tables
are really unique. So are the ones on the Parisi table, but not quite the same.

They are attribuited to or in the style of...
that doesn't really mean that they were designed by Gio Ponti or Ico and Luisa Parisi. It means that people think that maybe they were designed by one of these folks, but there is no solid proof. But both Parisi's and Ponti's works have been extensively researched and your furniture pieces are most likely not documented as theirs. This is a very common mistake that people do. Saying that this piece of furniture is designed by so and so is not the same with saying that this furniture piece is attribuited to so and so. In any case, your furniture is very cool. I would keep it if it came my way.

better yet...
Better yet, you should contact a reputable auction house such as Philips, Wright or elsewhere and they might be able to tell you if these are really Parisi or Ponti, but I doubt they are...Let us Know what you find out!

Thanks for your suggestions, EpocaModerna
I definitely agree that it's important to distinguish between attribution and documented designer. Of course, some unscrupulous or inexperienced sellers do not do this. But the proliferation of phrases like: "in the style of", "attributed to", "after" and "in the manner of" demonstrates the care that many dealers take not to mislead potential buyers in this way. I am very careful myself.
That said, I am still very curious as to who designed my tables. I will take your advice and contact some auction houses. Awhile ago, someone on this forum posted a list of the more prominent ones, which I found very helpful. I'm attaching the link to that post here in case others might find it helpful as well. I'll definitely post here when/if I find out who designed the tables. Thanks again.
http://www.designaddict.com/design_links/index.cfm/fuseaction/links_show...

An Update
I sent pictures to over 20 auction houses and no one knows who designed these tables. I got estimates of value anywhere from $200 to $2000. So I guess these will forever remain a mystery. Nice tables though...

It's been two years since I posted this query about these mystery tables. They are so cool, but I simply could not find out who made them. After posting on here, I followed people's advice and wrote to scores of auction houses in Europe. Surprisingly, no one recognized them. But most everyone agreed that they were Italian and certainly influenced by the Parisi's, who were in turn influenced by Gio Ponti. That's as far as I got. And I finally gave up.
But today I was trawling through Craigslist and I saw the same table! And there was a sticker on the back that said "Adams Always." What do you know? They're not Italian at all, but made in the good ole' U.S. of A.
I had to share this. I'm sure you have all been on the edge of your seats to know, as I have. I can't find any information at all about Adams Always, but this is still a red letter day!