  Nested sampling is an iterative integration procedure that shrinks the prior
volume towards higher likelihoods by removing a "live" point at a time. A
replacement point is drawn uniformly from the prior above an ever-increasing
likelihood threshold. Thus, the problem of drawing from a space above a certain
likelihood value arises naturally in nested sampling, making algorithms that
solve this problem a key ingredient to the nested sampling framework. If the
drawn points are distributed uniformly, the removal of a point shrinks the
volume in a well-understood way, and the integration of nested sampling is
unbiased. In this work, I develop a statistical test to check whether this is
the case. This "Shrinkage Test" is useful to verify nested sampling algorithms
in a controlled environment. I apply the shrinkage test to a test-problem, and
show that some existing algorithms fail to pass it due to over-optimisation. I
then demonstrate that a simple algorithm can be constructed which is robust
against this type of problem. This RADFRIENDS algorithm is, however,
inefficient in comparison to MULTINEST.
