  A new way to run nested sampling, combined with realistic MCMC proposals to
generate new live points, is presented. Nested sampling is run with a fixed
number of MCMC steps. Subsequently, snowballing nested sampling extends the run
to more and more live points. This stabilizes MCMC proposals over time, and
leads to pleasant properties, including that the number of live points and
number of MCMC steps do not have to be calibrated, that the evidence and
posterior approximation improves as more compute is added and can be diagnosed
with convergence diagnostics from the MCMC literature. Snowballing nested
sampling converges to a ``perfect'' nested sampling run with infinite number of
MCMC steps.
