Spindly Laburnum Tree

Hello.

When we moved in the laurel in the corner of the garden was a jungle. It was towering above the telephone wires. So we cut it right down and found this laburnum tree hiding in the middle. The tree did flower and has leaves, so seems to be ok. Is there anything I can do to help it or encourage it to grow more branches. Also in the the close up picture you will see a spindly branch that  is hanging down, should I chop this off?  Any help would be great. Thank you