Bushface
Deity
While using the tactics described above, try attacking in two widely-separated places with only a turn or two between your attacks. This works particularly well if your victim has an empire of which some part is a long way from your borders or is on another continent, by reducing the distance your troops have to travel (relatively slowly) through foreign territory to reach the enemy's last city. Sometimes the enemy will bring troops to meet your first attack and away from your intended second; you'll need Spies to see this.
Taking a hypothetical example from the real world map, if Ecuador ever wanted to capture Chile using Civ4 rules it would take a very long time to fight the whole length of Chile from north to south, whereas a few invasions by sea would do the job much quicker. There would be a further advantage in that the invaded country would be broken into separate fragments, preventing troop movement from one fragment to another and cutting each fragment off from resources in the others. Or on a broader scale, given that the USA has expanded to include Mexico and wanted to capture a state occupying all of South America, it would be quicker not to fight down from Mexico alone but to land other forces in Colombia, Brazil and Chile.
Taking a hypothetical example from the real world map, if Ecuador ever wanted to capture Chile using Civ4 rules it would take a very long time to fight the whole length of Chile from north to south, whereas a few invasions by sea would do the job much quicker. There would be a further advantage in that the invaded country would be broken into separate fragments, preventing troop movement from one fragment to another and cutting each fragment off from resources in the others. Or on a broader scale, given that the USA has expanded to include Mexico and wanted to capture a state occupying all of South America, it would be quicker not to fight down from Mexico alone but to land other forces in Colombia, Brazil and Chile.