This paper investigates how critical-peak pricing (CPP) affects households with different usage and income levels, with the goal of informing policy makers who are considering the implementation of CPP tariffs in the residential sector. Using a subset of data from the California Statewide Pricing Pilot of 2003-2004, average load change during summer events, annual percent bill change, and post-experiment satisfaction ratings are calculated across six customer segments, categorized by historical usage and income levels. Findings show that high-use customers respond significantly more in kW reduction than do low-use customers, while low-use customers save significantly more in percentage reduction of annual electricity bills than do high-use customers - results that challenge the strategy of targeting only high-use customers for CPP tariffs. Across income levels, average load and bill changes were statistically indistinguishable, as were satisfaction rates - results that are compatible with a strategy of full-scale implementation of CPP rates in the residential sector. Finally, the high-use customers earning less than $50,000 annually were the most likely of the groups to see bill increases - about 5% saw bill increases of 10% or more - suggesting that any residential CPP implementation might consider targeting this customer group for increased energy efficiency efforts.