Two design principles are used frequently in clinical trials: 1) A subject is "matched" or "paired" with a similar subject to reduce the chance that other variables obscure the primary comparison of interest. 2) A subject serves as his/her own control by "crossing over" from one treatment to another during the course of an experiment. There are situations in which it may be advantageous to use the two design principles - crossing over and matching - simultaneously. That is, it may be advantageous to conduct a "paired crossover design," in which each subject, while paired with a similar subject, crosses over and receives each experimental treatment. In this paper, we describe two clinical trials conducted by the National Heart, Lung and Blood Institute's Asthma Clinical Research Network that used a paired 2x2 crossover design. The Beta Adrenergic Response by GEnotype (BARGE) Study compared the effects of regular use of inhaled albuterol on mildly asthmatic patients with different genotypes at the 16th position of the beta-agonist receptor gene. The Smoking Modulates Outcomes of Glucocorticoid (SMOG) Therapy in Asthma Study evaluated the hypothesis that smoking reduces the response to inhaled corticosteroids. For such paired crossover designs, the primary parameter of interest is typically the treatment-by-pairing interaction term. In evaluating the relative efficiency of the paired 2x2 crossover design to two independent crossover designs with respect to this interaction term, we show that the paired 2x2 crossover design is more efficient if the correlations between the paired members on the same treatments are greater than their correlations on different treatments. This condition should hold in most circumstances, and therefore the paired crossover design deserves serious consideration for any clinical trial in which the crossing over and matching of subjects is deemed simultaneously beneficial.