Response-adaptive allocation designs refer to a class of designs where the probability an observation is assigned to a treatment is changed throughout an experiment based on the accrued responses. Such procedures result in random treatment sample sizes. Most of the current literature considers unconditional inference procedures in the analysis of response-adaptive allocation designs. The focus of this work is inference conditional on the observed treatment sample sizes. The inverse of information is a description of the large sample variance of the parameter estimates. A simple form for the conditional information relative to unconditional information is derived. It is found that conditional information can be greater than unconditional information. It is also shown that the variance of the conditional maximum likelihood estimate can be less than the variance of the unconditional maximum likelihood estimate. Finally, a conditional bootstrap procedure is developed that, in the majority of cases examined, resulted in narrower confidence intervals than relevant unconditional procedures.