Aneuploidy is a major source of gene dosage imbalance due to copy number alterations (CNA), and viable human trisomies are model disorders of altered gene expression. We study gene and allele-specific expression (ASE) of 9668 single-cell fibroblasts from trisomy 21 (T21) discordant twins and from mosaic T21, T18, T13 and T8. We examine 928 single cells with deep scRNAseq. Expected and observed overexpression of trisomic genes in trisomic vs. diploid bulk RNAseq is not detectable in trisomic vs. diploid single cells. Instead, for trisomic genes with low-to-average expression, their altered gene dosage is mainly due to the higher fraction of trisomic cells simultaneously expressing these genes, in agreement with a stochastic 2-state burst-like model of transcription. These results, confirmed in a further analysis of 8740 single fibroblasts with shallow scRNAseq, suggest that the specific transcriptional profile of each gene contributes to the phenotypic variability of trisomies. We propose an improved model to understand the effects of CNA and, generally, of gene regulation on gene dosage imbalance.