Seamless phase II/III clinical trials offer an efficient way to select an experimental treatment and perform confirmatory analysis within a single trial. However, combining the data from both stages in the final analysis can induce bias into the estimates of treatment effects. Methods for bias adjustment developed thus far have made restrictive assumptions about the design and selection rules followed. In order to address these shortcomings, we apply recent methodological advances to derive the uniformly minimum variance conditionally unbiased estimator for two-stage seamless phase II/III trials. Our framework allows for the precision of the treatment arm estimates to take arbitrary values, can be utilised for all treatments that are taken forward to phase III and is applicable when the decision to select or drop treatment arms is driven by a multiplicity-adjusted hypothesis testing procedure. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.