I just finished pruning my Red Bird-of-Paradise (Caesalpinia pulcherrima), taking off about 1/3 of the height. This helps to promote additional flowers in early October.
The keyword here is to prune lightly, not severely prune. By pruning carefully at this time, it will help your plants look better throughout the winter months instead of looking messy and overgrown. Light pruning will also enable your plants to produce some new growth before the weather cools down and most plants stop growing.
Another plant that this works well for is many of your Lantana species. Lantana often suffers frost damage in the winter (in zones 9 and below) and by pruning lightly, it will minimize the size of the unsightly frost damage in winter.
In general, this method of pruning works well for most summer-flowering shrubs and perennials.
If you’d like to learn more about pruning shrubs in the desert garden, I invite you to learn more about my popular online pruning workshop. I’ve helped countless people just like you learn how to maintain beautiful, flowering shrubs with pruning twice a year or less!