We study non-Boolean PCPs that have perfect completeness and read three positions from the proof. For the case when the proof consists of values from a domain of size d for some integer constant d = 2, we construct a non-adaptive PCP with perfect completeness and soundness d_{}^{ - i} + d_{}^2 + E, for any constant e > 0, and an adaptive PCP with perfect completeness and soundness d_{}^{ - i} + Ee, for any constant e > 0. The latter PCP can be converted into a non-adaptive PCP with perfect completeness and soundness d_{}^{ - i} + E, for any constant e > 0, where four positions are read from the proof. These results match the best known constructions for the case d = 2 and our proofs also show that the particular predicates we use in our PCPs are non-approximable beyond the random assignment threshold.