Parsimony haplotyping is the problem of finding a set of haplotypes of minimum cardinality that explains a given set of genotypes, where a genotype is explained by two haplotypes if it can be obtained as a combination of the two. This problem is NP-complete in the general case, but polynomially solvable for $(k,l)$<alternatives><inline-graphic xlink:type="simple" xlink:href="oosterwijk-ieq2-2352031.gif"/></alternatives> -bounded instances for certain $k$<alternatives> <inline-graphic xlink:type="simple" xlink:href="oosterwijk-ieq3-2352031.gif"/></alternatives> and $l$<alternatives><inline-graphic xlink:type="simple" xlink:href="oosterwijk-ieq4-2352031.gif"/> </alternatives>. Here, $k$<alternatives> <inline-graphic xlink:type="simple" xlink:href="oosterwijk-ieq5-2352031.gif"/></alternatives> denotes the maximum number of ambiguous sites in any genotype, and $l$<alternatives> <inline-graphic xlink:type="simple" xlink:href="oosterwijk-ieq6-2352031.gif"/></alternatives> is the maximum number of genotypes that are ambiguous at the same site. Only the complexity of the $(*,2)$<alternatives><inline-graphic xlink:type="simple" xlink:href="oosterwijk-ieq7-2352031.gif"/></alternatives> -bounded problem is still unknown, where $*$ <alternatives><inline-graphic xlink:type="simple" xlink:href="oosterwijk-ieq8-2352031.gif"/></alternatives> denotes no restriction. It has been proved that $(*,2)$<alternatives> <inline-graphic xlink:type="simple" xlink:href="oosterwijk-ieq9-2352031.gif"/></alternatives>-bounded instances have compatibility graphs that can be constructed from cliques and circuits by pasting along an edge. In this paper, we give a constructive proof of the fact that $(*,2)$<alternatives> <inline-graphic xlink:type="simple" xlink:href="oosterwijk-ieq10-2352031.gif"/></alternatives>-bounded instances are polynomially solvable if the compatibility graph is constructed by pasting cliques, trees and circuits along a bounded number of edges. We obtain this proof by solving a slightly generalized problem on circuits, trees and cliques respectively, and arguing that all possible combinations of optimal solutions for these graphs that are pasted along a bounded number of edges can be enumerated efficiently.