Dresser trays are small cast iron trays usually not bigger than 5-6 inches tall by 7 or 8 inches wide. One can easily distinguish a dresser tray by examizing their bottom. There are 3 or 4 short flat projections protuding from its surface. These projections allow the tray to sit, horizontally, on one's dresser.
Dresser Trays wiere intended to be a catch all holding the litte things such as bobby pins, money-coins, etc. -- whatever.was in one's pockets prior to retiring for bed. That is why the paint is rarely in great condition. because all those daily pocket items wore it off.
Note the 3 projections on the bottom of this Dresser Tray that stabilizes it on a horizontal surface.
One might think, these vessels could be ashtrays But, I don't think Bradley & Hubbard intended such a pretty painted surface to be destroyed by putting out a ciarette there. However, one version of "the Man & His Pipe" has a tabacco cutting device.