Danish Desk Restoration  

Damp
Damp cotton wool, and the tip of a hot iron should raise the dent.
Nice desk !

Dents?
I'd also like to learn about repairing dents. I own a Walnut desk with dents caused by metal springs from a bungee cord that the shipper used to secure the desk drawers. Argh.
Gorgeous desk, Woof!

Dented
Thank you both! This desk is enjoyable to look at, need to use it.
I just remembered there's a youtube video...I'll try to find it later. Not sure if it's ok for veneered woods thats already finished.

nice desk!
like the drawers.
personnally i would go easy on the ironing, especially as it is veneered.
the metal crossbars though should make a big difference.

Should be okay to use a...
Should be okay to use a clothes iron on a steam setting...try and use something in-between the iron and the wood...parchment paper works.
I have used this method to bring seemingly hopeless dents back to almost total flushness. Patience is the key.
Let us know how it goes.

Worry not?
Should I be concerned about the finish using the Iron trick?
It isn't a big concern, there's heavy wear from decades of use. Plus I'm sanding out the cig burns.

The ironing
trick uses moisture (steam) to "puff up" the compressed fibers. Heat alone is useless, as is the steam generated by a steam iron. A spot of water on the dent, a damp-to-wet clean cotton (knit) cloth, and a hot iron. Use the iron alone, briefly, to dry the area following the procedure.
This is reliable and safe on solid wood. Don't expect miracles on veneer, or on wood that has been torn. Also, the procedure can affect the way the area takes subsequent finish, especially stain. Clear finish usually goes on okay. Sanding the entire surface is the best prep for finish.

So far so good using the...
So far so good using the iron treatment. Very slight improvement. Time consuming with little results. Perhaps it's the excess moisture in the cloth brought about by a leaky iron (which should've been disposed of long ago). Found a large soldering iron, will try using that.
*will post before/after pics when the time comes

Fruitless
Spent a lot of time nursing the dents to no avail. From here, I'm going to consult with some local refinishers and see what we can do. Thanks for the advice/support! Pictures will spring up eventually.