Some of our trees have partially leafed. Would it help or harm to prune branches that have no leaves?

-- One is missing leaves on one side.

-- Another is missing leaves at the top.

-- A third treet had zero leaves last summer and now has leaves clumped around the trunk on the lowest branches.

We're wondering if pruning is a good idea for these pathetic-looking trees or if we should just let nature take its course. They have been in our garden since 2004.

Thanks for any advice.

LaurieDutch