Getting rid of 'new furniture' smell

[dustyspringfield]

I have a chest of draws - mixture of solid wood (the drawers) and veneer, but a couple of years on all our clothes still smell of that 'new furniture' smell - not just wood exactly, but I expect glue, varnish, whatever is inside the veneers. I aired it well before putting it together, but clearly to no effect. Just how long is it going to be smelly for??
Any ideas on what will get rid? I don't want to use anything chemical like fabreze.

[toomuchcoffeetoomuchwine]

Lavender bags?