Is there a succinct verb for the act of putting something on top of something else? I'm looking for something more vivid than a simple put or place.
I xxx'd the letter on the pile of bills.
How about "toss"? That was what my brain filled in when I read your sentence.
There's stacked, and you could say you added the letter to the pile.
Additional reference: http://www.youtube.com/watch?v=1f-kfRREA8M
I would say piled but that sounds bad in the context of your example. I'd choose between some flavor of stack or pile - "I piled the letter on top of all the bills" - and using some flavor of put or place - "I put the letter on the pile of bills".
stack - Arrange (a number of things) in a pile, typically a neat one: "the books had been stacked up in three piles".
put - Move to or place in a particular position: "Harry put down his cup"
You can use the verb lay (past tense laid).
Some variations with various nuances: