# Quasi-poisson for underdispersed data

Related to glm() in R, I saw a few post recommending modeling underdispersed data using the Conway–Maxwell–Poisson distribution, specifically with the R package CompGLM, however, I'm not sure I saw anybody confirming that the quasi-poisson cannot be used. Therefore, I ask: why not use quasi-poisson in glm for underdispersed data? After all, isn't the idea of quasi-poisson to go beyond the assumption that variance and mean are equal ? (and in the case of underdispersion, there are not equal).

Basically, I am running a glm(y~x,family=poisson) where x is a categorical variable and i am getting

Null deviance: 67.905  on 519  degrees of freedom
Residual deviance: 59.584  on 507  degrees of freedom


Which strongly suggest underdispersion and I am therefore leaning towards a quasi-poisson solution.