[R] binomial models with too many 1s???

[I.Szentirmai]

Dear R users,

Does anyone know a solution for the problem when there are 
too many ones or zeros in the respons of a binomial model? 
I think this means that the data are over/under despersed 
and the result is very bad model fit.

I'm using glmmPQL(family=quasibinomial) to fit a model to 
my data, but the model estimates are not in the range they 
should be due to overdispersion (or under?) What shall I 
do? Is there a model type for this kind of data? I would 
prefer to keep all may data, otherwise I could also select 
some of the ones so that their number will be equal to the 
number of zeros. But I don't thik this is the right way...

Any help would be appreciated.

Thanks,
Istvan