By reconciling the phylogenetic tree of a gene family with the corresponding species tree, it is possible to infer lineage-specific duplications and losses with high confidence and hence to annotate orthologs and paralogs. The currently available reconciliation methods for nonbinary gene trees are computationally expensive for genome-scale applications. We present four O (| G |+| S |) algorithms to reconcile an arbitrary gene tree G with a binary species tree S in the duplication, loss, duploss (also known as mutation), and deep coalescence cost models, where |· | denotes the number of nodes in a tree. The improvement is achieved through two innovations: a linear-time computation of compressed child-image subtrees and efficient reconstruction of irreducible duplication histories. Our technique for child-image subtree compression also results in an order of magnitude speedup in runtime for the dynamic programming and Wagner parsimony--based methods for tree reconciliation in the affine cost model.