  In this paper we define and examine the power of the {\em
conditional-sampling} oracle in the context of distribution-property testing.
The conditional-sampling oracle for a discrete distribution $\mu$ takes as
input a subset $S \subset [n]$ of the domain, and outputs a random sample $i
\in S$ drawn according to $\mu$, conditioned on $S$ (and independently of all
prior samples). The conditional-sampling oracle is a natural generalization of
the ordinary sampling oracle in which $S$ always equals $[n]$.
  We show that with the conditional-sampling oracle, testing uniformity,
testing identity to a known distribution, and testing any label-invariant
property of distributions is easier than with the ordinary sampling oracle. On
the other hand, we also show that for some distribution properties the
sample-complexity remains near-maximal even with conditional sampling.
