Using an (empirical) Bayesian multilevel model can both attach uncertainty intervals to the point estimates and appropriately "shrink" the estimates towards zero at the low-sample-size end.
The latter is more directly interpretable, at the cost of slightly more complex modelling (/assumptions).
Looking for explanation of multilevel model, I found http://mc-stan.org/documentation/case-studies/radon.html which seems to do exactly that in "Partial pooling model". (see graph)
Instead you'd want to use a CDF that bins that values.