A vertical co-product technology simultaneously produces multiple outputs that differ along a rankable quality metric. Co-product manufacturers often sell products through a distributor. We examine a setting in which a manufacturer sells vertically differentiated co-products through a self-interested distributor to quality-sensitive end customers. The manufacturer determines its production, product line design, and wholesale prices. The distributor determines its purchase quantities and retail prices. In traditional product-line design, products can be produced independently of each other and higher-quality products have higher production costs. This literature established that the length of the product line (i.e., difference 1 between highest and lowest qualities) is greater in an indirect channel than in a direct channel. By contrast, co-products cannot be produced independently of each other. Among other findings, we establish that this interdependency causes the opposite channel effect: for co-products, the length of the product line is smaller in an indirect channel than in a direct channel. Additionally, we show there exists a theoretical contract, combining revenue sharing and reverse slotting fees, that eliminates the indirect-channel distortions in both product line design and output quantities.