  We study the strength of a first-order electroweak phase transition in the
Inert Doublet Model (IDM), where particle dark matter (DM) is comprised of the
lightest neutral inert Higgs boson. We improve over previous studies in the
description and treatment of the finite-temperature effective potential and of
the electroweak phase transition. We focus on a set of benchmark models
inspired by the key mechanisms in the IDM leading to a viable dark matter
particle candidate, and illustrate how to enhance the strength of the
electroweak phase transition by adjusting the masses of the yet undiscovered
IDM Higgs states. We argue that across a variety of DM masses, obtaining a
strong enough first-order phase transition is a generic possibility in the IDM.
We find that due to direct dark matter searches and collider constraints, a
sufficiently strong transition and a thermal relic density matching the
universal DM abundance is possible only in the Higgs funnel regime.
