It's a trade off. Clopper-Pearson can be overly conservative in many instances. I tend to use Jeffreys interval personally, which is a Bayesian method.

Brown et al. give a formal treatment of the subject with simulations showing actual coverage probabilities for the various methods. It is worth a read if you want to really dive into the subject.

ref: Brown, Lawrence D.; Cai, T. Tony; DasGupta, Anirban (2001). "Interval Estimation for a Binomial Proportion". Statistical Science 16 (2): 101–133