Couple of comments. Don't till your beds, it breaks up the network of micro-organisms that are breaking down the compost materials and releasing nutrients used by plants and worms. When it gets broken up the process halts and so does the natural source of nutrients until it's had time to reconstruct the network. Second, it brings more weed seeds to the surface that you then have to manage. Wood mixed in with the dirt and compost (not counting branches, logs, and big pieces) sucks up all the available nitrogen as part of the decay process, therefore stealing it from vegetables. However, a thick layer of compost topped with a thick layer (4 inches) of wood chips made up of multi-sized pieces and includes the leaves and needles that were on the tree is an excellent thing to put on top of the beds. It's a super mulch, a sponge like described in that link, and it breaks down slowly over time adding rather than taking nutrients from the soil. If you want to add more compost, just toss some on top of the wood chips and water it in. It's best to add these layers in the fall to allow time for them to do their thing before you plant in the spring.
