Battle of Wake Island
The Battle of Wake Island, during World War II, took place in the aftermath of the Attack on Pearl Harbor. The Japanese attacked the island with its small American garrison. They were initially repulsed, and American leaders had to make the difficult decision of whether to try to reinforce the island.
In the end American leaders decided that trying to relieve the island exposed the fleet to too much risk, that if the Japanese were able to defeat them in detail the war could be prolonged or even lost. The garrison eventually surrendered and the Japanese killed most of the POWs.