Abstract1. One hypothesis explaining extra-pair reproduction is that socially monogamous females mate with extra-pair males to adjust the coefficient of inbreeding (f) of extra-pair offspring (EPO) relative to that of within-pair offspring (WPO) they would produce with their socially paired male. Such adjustment of offspring f requires non-random extra-pair reproduction with respect to relatedness, which is in turn often assumed to require some mechanism of explicit pre-copulatory or post-copulatory kin discrimination. 2. We propose three demographic processes that could potentially cause mean f to differ between individual females' EPO and WPO given random extra-pair reproduction with available males without necessarily requiring explicit kin discrimination. Specifically, such a difference could arise if social pairings formed non-randomly with respect to relatedness or persisted non-randomly with respect to relatedness, or if the distribution of relatedness between females and their sets of potential mates changed during the period through which social pairings persisted. 3. We used comprehensive pedigree and pairing data from free-living song sparrows (Melospiza melodia) to quantify these three processes and hence investigate how individual females could adjust mean offspring f through instantaneously random extra-pair reproduction. 4. Female song sparrows tended to form social pairings with unrelated or distantly related males slightly less frequently than expected given random pairing within the defined set of available males. Furthermore, social pairings between more closely related mates tended to be more likely to persist across years than social pairings between less closely related mates. However, these effects were small and the mean relatedness between females and their sets of potential extra-pair males did not change substantially across the years through which social pairings persisted. 5. Our framework and analyses illustrate how demographic and social structuring within populations might allow females to adjust mean f of offspring through random extra-pair reproduction without necessarily requiring explicit kin discrimination, implying that adjustment of offspring f might be an inevitable consequence of extra-pair reproduction. New theoretical and empirical studies are required to explore the general magnitude of such effects and quantify the degree to which they could facilitate or constrain long-term evolution of extra-pair reproduction.