  A large number of studies, all using Bayesian parameter inference from Markov
Chain Monte Carlo methods, have constrained the presence of a decaying dark
matter component. All such studies find a strong preference for either very
long-lived or very short-lived dark matter. However, in this letter, we
demonstrate that this preference is due to parameter volume effects that drive
the model towards the standard $\Lambda$CDM model, which is known to provide a
good fit to most observational data.
  Using profile likelihoods, which are free from volume effects, we instead
find that the best-fitting parameters are associated with an intermediate
regime where around $3 \%$ of cold dark matter decays just prior to
recombination. With two additional parameters, the model yields an overall
preference over the $\Lambda$CDM model of $\Delta \chi^2 \approx -2.8$ with
\textit{Planck} and BAO and $\Delta \chi^2 \approx -7.8$ with the SH0ES $H_0$
measurement, while only slightly alleviating the $H_0$ tension. Ultimately, our
results reveal that decaying dark matter is more viable than previously
assumed, and illustrate the dangers of relying exclusively on Bayesian
parameter inference when analysing extensions to the $\Lambda$CDM model.
