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

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... 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× 10^7 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× 10^7 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.