I'm working on the following model in R:

Generalized linear mixed model fit by maximum likelihood ['glmerMod']
  Family: binomial (logit)
  Formula: Tooluse ~ Sex + Age + Frequency + Tool.related.skill +
      (1|Trial) + (1 + Frequency|Subjectnumber) + 
      (1 + Tool.related.skill|Frequency/Task) 
  Data: g4      

with

• Tooluse (yes, no)
• age (continuous)
• tool.related.skill (ordinal)
• trial (1-4)
• frequency (low, high)
• task (1-12, nested within frequency. 6 tasks belong to the low frequency group, 6 tasks to high frequency)

My research question looks at the effect of the frequency variable on tool use.

Testing the model assumptions, I get this output for the test of overdispersion:

overdisp.test (B1NF.FULL)  
##       chisq     df    P   dispersion.parameter 
##    1 36.68702  141    1      0.2601916

How can I deal with the problem of underdispersion? So far I got 3 suggestions (2 of them from one of the authors of the lme4 package):

1. using mixture/hurdle models

2. allowing a negative correlation structure within groups (which can't be done with lme4 and is harder for GLMMs in general)

3. standard 'quasi-likelihood' approach, i.e. taking the estimated level of underdispersion and shrinking all the confidence intervals accordingly as a first approach. However, I got warned that the thing to be careful about there is that it has yet to be figured out how quasi-likelihood estimates of 'residual' variance interact with the estimates of the random effects variances

I would greatly appreciate any opinions and especially any help on how to implement any of these strategies in R. I feel kind of lost here.