For reference, from the Agresti and Coull (1998) paper above, I would also compare with the Clopper-Pearson interval. I didn't bother to run the calculation manually, but I found an R function binCI(n, y) that is supposed to do it (n = # observations and y = # of successes). In fact, it has facilities for a number of methods. I'll print them all. The output is below:

Code:

> binCI(40, 0, method = "CP") ## Clopper-Pearson
95 percent CP confidence interval
[ 0, 0.0881 ]
Point estimate 0
> binCI(40, 0, method = "AC") ## Agresti-Coull
95 percent AC confidence interval
[ -0.01677, 0.1044 ]
Point estimate 0
> binCI(40, 0, method = "Blaker") ## Blaker
95 percent Blaker confidence interval
[ 0, 0.0795 ]
Point estimate 0
> binCI(40, 0, method = "Score") ## Wilson Score
95 percent Score confidence interval
[ 0, 0.08762 ]
Point estimate 0
> binCI(40, 0, method = "SOC") ## Second-order corrected
95 percent SOC confidence interval
[ -0.005935, 0.05665 ]
Point estimate 0
> binCI(40, 0, method = "Wald") ## Wald
95 percent Wald confidence interval
[ 0, 0 ]
Point estimate 0

As the paper details, the CP interval does not perform very well, but it is an alternative to the basic. Note, I don't know half the methods used above or their appropriateness. Nor do I know if the function even works correctly. If you're interested, find their formulas and check them manually. I only leave this as reference.