  We analyse a mathematical model of seeding for sports contests with
round-robin qualifying tournaments. The standard seeding system based on
coefficients measuring the historical performance of the teams is shown to be
unfair as it might potentially punish a team for its better results by having
to face stronger opponents on average in the next stage. Major football
competitions are revealed to suffer from this weakness. Incentive compatibility
can be guaranteed by providing each qualified team with the highest coefficient
of all teams that are ranked lower in its qualifying tournament for seeding
purposes. Our proposal is illustrated by the 2020/21 UEFA Champions League.
