We study a very basic open problem regarding the PCP characterization of NP, namely, the power of PCPs with non-adaptive queries and perfect completeness. The lowest soundness known till now for such a PCP is \frac{6}{8} + \in given by a construction of H?astad [11]. However, Zwick [15] shows that a -query non-adaptive PCP with perfect completeness cannot achieve soundness below \frac{5}{8}.