Genomic changes such as copy number alterations are one of the major underlying causes of human phenotypic variation among normal and disease subjects. Array comparative genomic hybridization (CGH) technology was developed to detect copy number changes in a high-throughput fashion. However, this technology provides only a >30-kb resolution, which limits the ability to detect copy number alterations spanning small regions. Higher resolution technologies such as single nucleotide polymorphism (SNP) microarrays allow detection of copy number alterations at least as small as several thousand base pairs. Unfortunately, strong probe effects and variation introduced by sample preparation procedures have made single-point copy number estimates too imprecise to be useful. Various groups have proposed statistical procedures that pool data from neighboring locations to successfully improve precision. However, these procedure need to average across relatively large regions to work effectively, thus greatly reducing resolution. Recently, regression-type models that account for probe effects have been proposed and appear to improve accuracy as well as precision. In this paper, we propose a mixture model solution, specifically designed for single-point estimation, that provides various advantages over the existing methodology. We use a 314-sample database, to motivate and fit models for the conditional distribution of the observed intensities given allele-specific copy number. We can then compute posterior probabilities that provide a useful prediction rule as well as a confidence measure for each call. Software to implement this procedure will be available in the Bioconductor oligo package (www.bioconductor.org).