Plasmid loss rate measurements are standard in microbiology and key to understanding plasmid stabilization mechanisms. The conventional assays eliminate selection for plasmids at the beginning of the experiment and screen for the appearance of plasmid-free cells over long-term population growth. However, it has been long appreciated in plasmid biology that the growth rate differential between plasmid-free and plasmid-containing cells at some point overshadows the effect of primary loss events, such that the assays can greatly over-estimate inherent loss rates. The standard solutions to this problem are to either consider the very early phase of loss where the fraction of plasmid-free cells increases linearly, or to measure the growth rate difference either by following the population for longer time or by measuring growth rates separately. Here we mathematically show that in all these cases, seemingly small experimental errors in the growth rate estimates can overshadow the estimates of the loss rates. For many plasmids, loss rates may thus be much lower than previously thought, and for some plasmids, the estimated loss rate may have nothing to do with actual loss rates. We further modify two independent experimental methods to separate inherent losses from growth differences and apply them to the same plasmids. First we use a high-throughput microscopy-based approach to screen for plasmid-free cells at extremely short time scales--tens of minutes rather than tens of generations--and apply it to a par⁻ version of mini-R1. Second we modify a counterselection-based plasmid loss assay inspired by the Luria-Delbrück fluctuation test that completely separates losses from growth, and apply it to various R1 and pSC101 derivatives. Concordant results from the two assays suggest that plasmids are lost at a lower frequency than previously believed. In fact, for par⁻ mini-R1 the observed loss rate of about 10⁻³ per cell and generation seems to be so low as to be inconsistent with what we know about the R1 stabilization mechanisms, suggesting these well characterized plasmids may have some additional and so far unknown stabilization mechanisms, for example improving copy number control or partitioning at cell division.