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 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.
However, one version of "the Man & His Pipe" has a tabacco cutting device,