I grew up in Whitman County hunting birds without a dog. I did very well - in good years I would take over 100 roosters, alone. You need to hunt country conducive to hunting without a dog, though. Focus on the bottom of canyons/draws, narrow or smaller thick patches of "red brush", the scab rock country, brush under bluffs, etc.
Stay away from the real open country and if possilbe, approach your target area from a direction that shields your approach.
Someone mentioned changing your pace from time to time - this works as well.