Combining several approaches would be the most effective way, however
if you have symptoms such as cough, wheeze and chest tightness or have frequent emergency room visits and hospitalizations, you should focus on reducing the symptoms.
Alternative treatment for asthma falls into two categories.
One is about diet and foods.
This includes anti-candida diet, nutritional supplements (magnesium, vitamin C, vitamin E, beta carotene, omega3, zinc), foods which are high in the nutrients I listed above.
The other is about physical therapy.
This includes breathing technique, yoga, qigong and tai chi chuan, but remember, as I said above, you should concentrate on relieving airway inflammation while you have symptoms, frequent emergency room visits and hospitalizations.
Have you read 'Reversing Asthma' by Richard N. Firshein?
This is a very informative and helpful book which details alternative treatments for asthma, but the author stresses the important role which asthma medications play as a life saver.
Also, I believe that peak flow reading would be very helpful for preventing asthma attacks and monitoring your airway conditions.