In several of the stories, Alexie uses black humor and comedy to deal with the oppression. We also see irony used a lot. For example in "Thomas Builds a Fire" the main character is sent to jail for life for a murder committed over 150 years ago. Additionally, the language which Alexie uses is often times sarcastic. Additionally, the author often, but not always, portrays the white men as being powerful but yet still somewhat stupid. We see this in the story "Indian Education"
Alexie also uses the imagination and the power of imagination to help the characters deal with the loss of power that the Indians on the reservation experience. Since they cannot win a battle with the white man - they live in a world of illusions as a coping mechanism. Here the power of the white man has no influence and only in the realm of imagination can the characters be free.
It is also significant that the white characters who are peppered throughout the book are not usually named. In a way, the author using the idea of having a name and connecting it with having an identity. The whites in the stories represent power but as they do not have names, they are not important as people to the Indian characters.