Four double-blind, randomised, placebo-controlled clinical trials of asthma or rhinitis treated with homeopathic immunotherapy (HIT) at a 30C potency have been published. The most recent study, involving house dust mite allergic asthmatics, failed to confirm a therapeutic improvement at the end of the study, but did provide preliminary evidence for an oscillation in outcome (both physiological and subjective) in with verum treatment to placebo. In this paper we show how such an oscillation is consistent with a complexity theory interpretation of how the body functions as a whole, and speculate on why different studies have produced different results. If the complexity theory interpretation is correct, then this will have a significant impact on the design of clinical trials in homeopathy and, possibly, other complementary medical interventions.