A slow dripping noise will help attract birds. The leaves will attract insects and provide food for foraging birds. Or place the leaves right in the garden to compost so that you will not have to move the decayed brown gold. You can easily turn in or mulch with the composted leaves right on the spot. Save time by not pruning all dead branches.
Birds like to perch and view an area before sampling food and water.
Besides, it is easier to see birds next summer if you have a few branches without leaves. Use plants or fences to create a south-facing windbreak. DON'T use systemic pesticides such as Dimethoate, which can poison birds eating the berries. Instead, try hosing off the plant and then use an insecticidal soap or superior oil. Save time by letting a dead tree that does not threaten your home stand in your naturescape.