Normally, it's wise to keep the drawers within your dresser while it's being moved
Even though the dresser is slightly heavier for the movers to carry with the drawers kept in it, they only have to make one trip with it rather than making a trip with it and then numerous more trips with each of its drawers. Snugly padding a dresser and securing the pads with tape will hold the drawers in place so that they don't fall out during moving.
Mirrors (if any) should be removed before padding a dresser
Mirrors should be seperately wrapped in pads and boxed for transport. But if there's any glass / mirrors set into the finish of the dresser then flattened cardboard should be taped over the part of the pad that's covering the inlays. This will protect glass and protect marble and will signal each of your movers handling dresser as to where the glass is under the blanket so that they'll be careful not to put pressure on it and break it.
Before moving a chest of drawers it's always best to empty its drawers entirely.
At least empty them entirely of small loose or breakable objects like trinkets because they will fly out when you're moving a chest of drawers as it is tipped to go up / down stairs, thru doorways or on / off the truck. If you want to leave some lighter clothing items in the drawers when moving it you should only leave things like shirts, undergarments, socks, etc.
Take notice that any extra weight in the dresser's drawers can put adverse pressure
It may seem better to you to just leave all of the contents in the drawers and pull them out and use them like boxes to carry those things. In some situations it may actually be easier to do this rather than to pack the things from the drawers into boxes and then unpack them later and put them back into the drawers. In such a case, go ahead and take these drawers full of stuff out of the dresser and make your multiple trips. It's a judgement call on the part of of the people actually doing the moving as to which is easier.
However, if you do put the full drawers back into the dresser when it gets onto the truck, bear in mind that you could damage the drawer's glides, since the weight of the drawer will be bounced on its glides within the dresser by the movement of the truck.
And remember - if you take the drawers and their contents out of the dresser, then you have to put them somewhere on the truck in such a way that the contents don't get shaken out of the drawers while the truck is moving. You could put the drawers into a van or a car to solve this problem because it travels smoother than a truck. You could also plastic wrap them for transport on the truck to hold all of their goods inside.
Also remember that while carrying the drawers seperately it is easy to scratch or gouge the finish on the front of them so be very careful.
It is our conclusion that it is almost always best to just empty the drawers
Next, the photo sequence on the left will show you how-to pad a dresser to hold its drawers in place and protect its finish while it's being moved. You start by putting one or two large moving blankets over the top of the dresser, draping them down over the sides, front and back, past the bottom.
Then diaper the dresser by using movers packing tape tightly wrapped around the pads to hold them firmly in place during moving. Only allow the tape to stick to the blankets - not to the finish of the dresser since this could damage it by leaving hard to remove tape residue.
Tape the blankets snugly to the front, sides, and back of the dresser by winding the tape 4 or more times around it, circling the piece repeatedly from top to bottom. Then tip the dresser up and tape the padding under its bottom. In this manner the blankets will stay firmly over, around, and under the dresser, fully protecting it.
The purpose of padding under the dresser is so that you can easily slide it on the truck
If the dresser is a high-boy then first set a pad down on the floor and set the dresser centered upon it. Next, lift the pad and tape it snugly around the sides, front and back to hold it up. Only allow the tape to touch the pad, not the dresser's finish so as to avoid tape residue damage. Then do the padding mentioned above from the top down and tape the top pad(s) securely to the bottom pad so neither will come loose during the move.
These securely snugged pads - top and bottom - will thoroughly protect the dresser
Further instruction on the best way to lift a dresser and carry it or to dolly a dresser will be made available to you upon subscription to the site.