Poststratification is a common method of estimation in household surveys. Cells are formed based on characteristics that are known for all sample respondents and for which external control counts are available from a census or another source. The inverses of the poststratification adjustments are usually referred to as coverage ratios. Coverage of some demographic groups may be substantially below 100 percent, and poststratifying serves to correct for biases due to poor coverage. A standard procedure in poststratification is to collapse or combine cells when the sample sizes fall below some minimum or the weight adjustments are above some maximum. Collapsing can either increase or decrease the variance of an estimate but may simultaneously increase its bias. We study the effects on bias and variance of this type of dynamic cell collapsing theoretically and through simulation using a population based on the 2003 National Health Interview Survey. Two alternative estimators are also proposed that restrict the size of weight adjustments when cells are collapsed.