Association studies that genotype affected offspring and their parents (triads) offer robustness to genetic population structure while enabling assessments of maternal effects, parent-of-origin effects, and gene-by-environment interaction. We propose case-parents designs that use pooled DNA specimens to make economical use of limited available specimens. One can markedly reduce the number of genotyping assays required by randomly partitioning the case-parent triads into pooling sets of h triads each and creating three pools from every pooling set, one pool each for mothers, fathers, and offspring. Maximum-likelihood estimation of relative risk parameters proceeds via log-linear modeling using the expectation-maximization algorithm. The approach can assess offspring and maternal genetic effects and accommodate genotyping errors and missing genotypes. We compare the power of our proposed analysis for testing offspring and maternal genetic effects to that based on a difference approach and that of the gold standard based on individual genotypes, under a range of allele frequencies, missing parent proportions, and genotyping error rates. Power calculations show that the pooling strategies cause only modest reductions in power if genotyping errors are low, while reducing genotyping costs and conserving limited specimens.