In reply to Ksharp.

Yes, the distribution of the p-values depends on many things, including the difference between the data and the model (which includes the size of the effect) and the power of the test. You can imagine that is the data are from N(72, 10) and the model tests for μ=72.01, that the distribution of p-values is ALMOST uniform. Versus if you are testing for μ=100.