Provided herein are water-soluble prodrugs, compositions comprising such prodrugs, and related methods of making and administering the same. The prodrugs of the invention comprise a water-soluble polymer having three or more arms, at least three of which are typically covalently attached to an active agent, e.g., a small molecule. The conjugates of the invention provide an optimal balance of polymer size and structure for achieving improved drug loading, since the conjugates of the invention possess three or more active agents releasably attached to a multi-armed water-soluble polymer. The prodrugs of the invention are therapeutically effective, and exhibit improved properties in-vivo when compared to unmodified parent drug.