Draping is a good temporary solution. Around a large planting, netting may need to be high enough to prevent being jumped over. This is a height of six to eight feet or more. At this point, of course, it's really a fence. A four foot wire fence with an electrified strand near the top can be quite effective.
Deer learn to fear it.
A nearby planting surrounded by a wire not electrified is usually left unmolested. Birds may be electrocuted if care is not taken when constructing the fence. Electrified fences will also keep out other pests such as raccoons, opossums, and squirrels. More information and construction suggestions can be found on Tom Clothier's pages. The issues with fencing are height and material.