An engine has a cylinder head with a deck face defining first and second chambers adjacent to one another and separated by a bore bridge. The body defines a first cooling jacket and a second cooling jacket configured to operate at a lower pressure than the first cooling jacket. The first cooling jacket is positioned substantially between the deck face and the second cooling jacket. The first cooling jacket has a series of passages intersecting the deck face and configured to receive coolant from a cylinder block cooling jacket. The second cooling jacket has an inlet passage intersecting the deck face adjacent to the bore bridge and configured to receive coolant from the cylinder block cooling jacket to cool the bore bridge.