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We compare four conditional tests for Poisson data through a simulation study: the exact binomial test, its asymptotic approximation, a Markov Chain Monte Carlo test and the standard permutation test. Despite being non-parametric, we observe that permutation tests are as effective as the others. From a theoretical point of view we justify this result by observing that the orbits of permutations form a \emph{good} partition of the conditional space.