I have a laburnum that has grown from seed to about six foot high and half inch thick at the soil level. It has no branches. although side shoots every spring. If I remove support, it whips about. Should I cut the top off to get it to thicken and branch?
I would consider placing your Laburnum onto a trellis.
You can grow it much like you would a Wisteria Vine.
It is best to grow it with one leader and they generally do not need pruning.