Allelic expression (AE) imbalance between the two alleles of a gene can be used to detect cis-acting regulatory SNPs (rSNPs) in individuals heterozygous for a transcribed SNP (tSNP). In this paper, we propose three tests for AE analysis focusing on phase-unknown data and any degree of linkage disequilibrium (LD) between the rSNP and tSNP: a test based on the minimum P-value of a one-sided F test and a two-sided t test (proposed previously for phase-unknown data), a test the combines the F and t tests, and a mixture-model-based test. We compare these three tests to the F and t tests and an existing regression-based test for phase-known data. We show that the ranking of the tests based on power depends most strongly on the magnitude of the LD between the rSNP and tSNP. For phase-unknown data, we find that under a range of scenarios, our proposed tests have higher power than the F and t tests when LD between the rSNP and tSNP is moderate (∼0.2<<∼0.8). We further demonstrate that the presence of a second ungenotyped rSNP almost never invalidates the proposed tests nor substantially changes their power rankings. For detection of cis-acting regulatory SNPs using phase-unknown AE data, we recommend the F test when the rSNP and tSNP are in or near linkage equilibrium (<0.2); the t test when the two SNPs are in strong LD (<0.7); and the mixture-model-based test for intermediate LD levels (0.2<<0.7).