  Taking on a new perspective of the electroweak phase transition, we
investigate in detail the role played by the depth of the electroweak minimum
("vacuum energy difference"). We find a strong correlation between the vacuum
energy difference and the strength of the phase transition. This correlation
only breaks down if a negative eigenvalue develops upon thermal corrections in
the squared scalar mass matrix in the broken vacuum before the critical
temperature. As a result the scalar fields slide across field space toward the
symmetric vacuum, often causing a significantly weakened phase transition.
Phenomenological constraints are found to strongly disfavour such sliding
scalar scenarios. For several popular models, we suggest numerical bounds that
guarantee a strong first order electroweak phase transition. The zero
temperature phenomenology can then be studied in these parameter regions
without the need for any finite temperature calculations. For almost all
non-supersymmetric models with phenomenologically viable parameter points, we
find a strong phase transition is guaranteed if the vacuum energy difference is
greater than $-8.8\times 10^7$~\text{GeV}$^4$. For the GNMSSM, we guarantee a
strong phase transition for phenomenologically viable parameter points if the
vacuum energy difference is greater than $-6.9\times 10^7$~\text{GeV}$^4$.
Alternatively, we capture more of the parameter space exhibiting a strong phase
transition if we impose a simultaneous bound on the vacuum energy difference
and the singlet mass.
