We present a model for genome size evolution that takes into account both local mutations such as small insertions and small deletions, and large chromosomal rearrangements such as duplications and large deletions. We introduce the possibility of undergoing several mutations within one generation. The model, albeit minimalist, reveals a non-trivial spontaneous dynamics of genome size: in the absence of selection, an arbitrary large part of genomes remains beneath a finite size, even for a duplication rate 2.6-fold higher than the rate of large deletions, and even if there is also a systematic bias toward small insertions compared to small deletions. Specifically, we show that the condition of existence of an asymptotic stationary distribution for genome size non-trivially depends on the rates and mean sizes of the different mutation types. We also give upper bounds for the median and other quantiles of the genome size distribution, and argue that these bounds cannot be overcome by selection. Taken together, our results show that the spontaneous dynamics of genome size naturally prevents it from growing infinitely, even in cases where intuition would suggest an infinite growth. Using quantitative numerical examples, we show that, in practice, a shrinkage bias appears very quickly in genomes undergoing mutation accumulation, even though DNA gains and losses appear to be perfectly symmetrical at first sight. We discuss this spontaneous dynamics in the light of the other evolutionary forces 123 2250 S. Fischer et al. proposed in the literature and argue that it provides them a stability-related size limit below which they can act.