Currently, quantitative RNA-seq methods are pushed to work with increasingly small starting amounts of RNA that require amplification. However, it is unclear how much noise or bias amplification introduces and how this affects precision and accuracy of RNA quantification. To assess the effects of amplification, reads that originated from the same RNA molecule (PCR-duplicates) need to be identified. Computationally, read duplicates are defined by their mapping position, which does not distinguish PCR- from natural duplicates and hence it is unclear how to treat duplicated reads. Here, we generate and analyse RNA-seq data sets prepared using three different protocols (Smart-Seq, TruSeq and UMI-seq). We find that a large fraction of computationally identified read duplicates are not PCR duplicates and can be explained by sampling and fragmentation bias. Consequently, the computational removal of duplicates does improve neither accuracy nor precision and can actually worsen the power and the False Discovery Rate (FDR) for differential gene expression. Even when duplicates are experimentally identified by unique molecular identifiers (UMIs), power and FDR are only mildly improved. However, the pooling of samples as made possible by the early barcoding of the UMI-protocol leads to an appreciable increase in the power to detect differentially expressed genes.