Copy-number variants (CNVs) form an abundant class of genetic variation with a presumed widespread impact on individual traits. While recent advances, such as the population-scale sequencing of human genomes, facilitated the fine-scale mapping of CNVs, the phenotypic impact of most of these CNVs remains unclear. By relating copy-number genotypes to transcriptome sequencing data, we have evaluated the impact of CNVs, mapped at fine scale, on gene expression. Based on data from 129 individuals with ancestry from two populations, we identified CNVs associated with the expression of 110 genes, with 13% of the associations involving complex, multiallelic CNVs. Categorization of CNVs according to variant type, size, and gene overlap enabled us to examine the impact of different CNV classes on expression variation. While many small (<4 kb) CNVs were associated with expression variation, overall we observed an enrichment of large duplications and deletions, including large intergenic CNVs, relative to the entire set of expression-associated CNVs. Furthermore, the copy number of genes intersecting with CNVs typically correlated positively with the genes' expression, and also was more strongly correlated with expression than nearby single nucleotide polymorphisms, suggesting a frequent causal role of CNVs in expression quantitative trait loci (eQTLs). We also elucidated unexpected cases of negative correlations between copy number and expression by assessing the CNVs' effects on the structure and regulation of genes. Finally, we examined dosage compensation of transcript levels. Our results suggest that association studies can gain in resolution and power by including fine-scale CNV information, such as those obtained from population-scale sequencing.