LIBERTY MOVING & STORAGE INC

Definitely DO allow them to use plastic wrap on dressers and desks. Needless to say, loose and fragile items should be packed well ahead of time but fabric and  paper items in don't have to be removed from normal storage devices like file cabinets, wardrobes, etc.
Don't get overly worried if they are a few minutes late. They start counting time (for billing) after they show up and get oriented to the job.

I trusted them to pack and move me across the country and they packed all my expensive breakables without bubble wrap. They put them in cardboard boxes, stacking one expensive plate on top of the other. Of course, many of my breakables arrived shattered. When I submitted my claim, they tried to say they used bubble wrap even though both I had specifically asked them to use bubble wrap and they said they didn't have any. 
They scratched up a near-perfectly finished 1940's antique sideboard and dining table. They won't pay to have it repaired. They packed expensive lamp shades at the bottom of boxes, unwrapped since they did not bring bubble wrap, and piled books on top of them. Of course, the lamp shades arrived scratched and smashed but they are refusing to pay for them.
Even though I have photos of all the breakage, and it was a lot, they are refusing to pay for the damage.
There was at least one box that did not show up at all and it contained very expensive lamps and a Gucci purse and mysteriously they don't know where it is and are refusing to cover it as well. 
I am contacting the Better Business Bureau and the Illinois Chamber of Commerce about them as well. I have had other clients of theirs contact me to say they also did not receive their belongings and are pursuing action through the appropriate legal and government channels.