Bursty gene expression is quantified by two intuitive parameters: the burst frequency and the burst size. While these parameters are known to be cell-cycle dependent for some genes, a transcriptome-wide picture remains missing. Here we address this question by fitting a suite of mechanistic models of gene expression to mRNA count data for thousands of mouse genes, obtained by sequencing of single cells for which the cell-cycle position has been inferred using a deep-learning approach. This leads to the estimation of the burst frequency and size per allele in the G1 and G2/M cell-cycle phases, hence providing insight into the global patterns of transcriptional regulation. In particular, we identify an interesting balancing mechanism: on average, upon DNA replication, the burst frequency decreases by≈50%, while the burst size increases by the same amount. We also show that for accurate estimation of the ratio of burst parameters in the G1 and G2/M phases, mechanistic models must explicitly account for gene copy number differences between cells but, surprisingly, additional corrections for extrinsic noise due to the coupling of transcription to cell age within the cell cycle or technical noise due to imperfect capture of RNA molecules in sequencing experiments are unnecessary.