Dame's Rocket is beautiful in the spring. Such pretty clusters of purple flowers like lilacs. Mine reseed easily. However, after the blooms are gone, they look like this.
Most of the dame's rocket in my garden are mixed in with other plants so the spindlyness isn't as obvious but this patch around one of the clothes line poles has only dame's rocket.
I'm letting the seeds form. Each little spine contains seeds. The house finches like to eat them right off the stalk. I know it's time to cut down the dame's rocket when I find the house finches feasting. I just cut them off at the ground and lay the stalks down where I want dame's rocket to grow again.