If a man or woman with asthma is to be in a clean environment, that means the spouse or other people in the house must quit smoking completely. Smoking confined in the garage or in the basement may help, but smoke will still find its way into the house, especially on the clothes of the smoker. Woman have contracted fatal asbestos disease from cleaning the asbestos-laden clothes brought home by their husbands. This is a silent killer if ever there was one. This problem is rare today, but don't discount something your spouse may be bringing home.
Many people are sensitive to allergens given off by cockroaches.
This is a particular problem in the south, where cockroaches are more prevalent. But choose your exterminator carefully. Many asthmatics also react to insecticide. If you have asthma and are concerned that something in the house may be triggering attacks, consult an allergist. But a word of caution.