Parent-of-origin (or imprinting) effects relate to the situation in which traits are influenced by the allele inherited from only one parent and the allele from the other parent has little or no effect. Given SNP genotype data from case-parent trios, the parent of origin of each allele in the offspring can often be deduced unambiguously; however, this is not true when all three individuals are heterozygous. Most existing methods for investigating parent-of-origin effects operate on a SNP-by-SNP basis and either perform some sort of averaging over the possible parental transmissions or else discard ambiguous trios. If the correct parent of origin at a SNP could be determined, this would provide extra information and increase the power for detecting the effects of imprinting. We propose making use of the surrounding SNP information, via haplotype estimation, to improve estimation of parent of origin at a test SNP for case-parent trios, case-mother duos, and case-father duos. This extra information is then used in a multinomial modeling approach for estimating parent-of-origin effects at the test SNP. We show through computer simulations that our approach has increased power over previous approaches, particularly when the data consist only of duos. We apply our method to two real datasets and find a decrease in significance of p values in genomic regions previously thought to possibly harbor imprinting effects, thus weakening the evidence that such effects actually exist in these regions, although some regions retain evidence of significant effects.