We present results from a series of experiments that allow us to measure overbidding and, in particular, underbidding in first-price auctions. We investigate how the amount of underbidding depends on seemingly innocent parameters of the experimental setup. To structure our data we present and test a theory of constant markdown bids. While a fraction of bidders can be well described by Bayesian Nash equilibrium bids, a larger fraction seems to either use constant markdown bids or seems to rationally optimise against a population where some members use markdown bids and some are rational.