The usual approach to the computation of cosmological phase transitions (PT) in thermal field
theory is through the construction of a dimensionally reduced effective field theory (3D EFT).
The need for robust theoretical predictions of the gravitational wave (GW) spectra sourced by
a first-order PT in the early Universe has recently pushed the construction of these 3D EFTs to
unprecedented levels of precision in loops. However, as far as the authors know, the contributions
from higher-dimensional effective operators that arise at the same order have generally been
neglected in the literature. Here, we perform a quantitative analysis of the impact of effective
interactions on the determination of PT parameters, and we develop a framework to consistently
compute them. We find that they allow for strong PTs in a wider region of parameter space, and
that both the peak energy density and frequency of the resulting GW power spectrum can change
by more than one order of magnitude when they are included.