John wrote:

No - the end of the leaves are yellow, and there are no cones at all.
The top is rounded. It branches upwards (?45%)- trunk darkish brown.

Great! You've got a Lawson cypress - in the summer the tips go yellow.
Female as well and trunk matches. Also, I looked at your second
picture, which I had first missed, and I am now convinced it's a
cypress.

As for pruning there's lots of way: reducing it (heading back),
thinning it or crown lifting it ... The choice is yours. However
lawson's don't like pruning, only lightly, as they don't reproduce new
branches (new buds). How many trunks do you have? You could perhaps
remove one or two if you need to make it look 'lighter'. HTH