  The dynamics of phase transitions (PT) in quantum field theories at finite
temperature is most accurately described within the framework of dimensional
reduction. In this framework, thermodynamic quantities are computed within the
3-dimensional effective field theory (EFT) that results from integrating out
the high-temperature Matsubara modes. However, strong-enough PTs, observable in
gravitational wave (GW) detectors, occur often nearby the limit of validity of
the EFT, where effective operators can no longer be neglected. Here, we perform
a quantitative analysis of the impact of these interactions on the
determination of PT parameters. We find that they allow for strong PTs in a
wider region of parameter space, and that both the peak frequency and the
amplitude of the resulting GW power spectrum can change by more than one order
of magnitude when they are included. As a byproduct of this work, we derive
equations for computing the bounce solution in the presence of
higher-derivative terms, consistently with the EFT power counting.
