We report a lab experiment to study subjects’ preferences over their ordinal rank in an earnings distribution. Following an assignment of unequal earnings, subjects can select a monetary transfer from exactly one individual to another, not including themselves. This can potentially change their own position in the distribution, as well as influence overall inequality. The experiment varies whether the initial earnings assignment is random or is affected by preliminary competition. It also varies the reference group from a complete to a partial network. A majority of observed transfers reduce inequality by moving earnings from those with the highest rank to the lowest rank in the distribution. Rank-improving transfers are substantially more common for preliminary competition losers than winners. Transfers to individuals outside of the reference group are not uncommon, and they usually target as the source the individuals high in the income distribution. While generally weak overall, own rank preferences appear to be more common among men than women.