A population genetics model of the role of asymmetric pairing and unequal exchange in the stabilization of transposable element copy number in natural populations is proposed and analysed. Monte Carlo simulations indicate that the approximations incorporated into the analysis are robust in the relevant parameter ranges. Given several simple assumptions concerning transposition and excision, equal and unequal exchange, and chromosome structure, predictions of the relative numbers of transposable elements in various regions of the Drosophila melanogaster genome are compared to the observed distribution of roo/B104 elements across chromosomal regions with differing rates of exchange, and between X chromosomes and autosomes. There is no indication of an accumulation of elements in the distal regions of chromosomes, which is expected if unequal exchange is reduced concomitantly with normal crossing over in the distal regions. There is, however, an indication of an excess of elements relative to physical length in the proximal regions of the chromosomes, which also have restricted crossing over. This observation is qualitatively consistent with the model's predictions. The observed distribution of elements between the mid-sections of the X chromosomes and autosomes is consistent with the predictions of one of two models of unequal exchange.