Various local hidden variables models for the singlet correlations exploit the detection loophole, or other loopholes connected with post-selection on coincident arrival times. I consider the connection with a probabilistic simulation technique called rejection-sampling, and pose some natural questions concerning what can be achieved and what cannot be achieved with local (or distributed) rejection sampling. In particular a new and more serious loophole, which we call the coincidence loophole, is introduced.

v.2: 7pp; conjecture 1 disproved by Gisin & Gisin (1999) but which leads to new open problems and conjectures. v.3: minor correction and addition. To appear in proceedings of "Quantum Probability and Infinite Dimensional Analysis", Greifswald, 2003; World Scientific. v.4: major revision in view of solution of another conjecture by Larsson & Gill (2003)