Crystal engineering principles were used to design three new co-crystals of paracetamol. A variety of potential co-crystal formers were initially identified from a search of the Cambridge Structural Database for molecules with complementary hydrogen-bond forming functionalities. Subsequent screening by powder X-ray diffraction of the products of the reaction of this library of molecules with paracetamol led to the discovery of new binary crystalline phases of paracetamol with trans-1,4-diaminocyclohexane (1); trans-1,4-di(4-pyridyl)ethylene (2); and 1,2-bis(4-pyridyl) ethane (3). The co-crystals were characterized by IR spectroscopy, differential scanning calorimetry, and H-1 NMR spectroscopy. Single crystal X-ray structure analysis reveals that in all three co-crystals the co-crystal formers (CCF) are hydrogen bonded to the paracetamol molecules through O-H center dot center dot center dot N interactions. In co-crystals (1) and (2) the CCFs are interleaved between the chains of paracetamol molecules, while in co-crystal (3) there is an additional N-H center dot center dot center dot N hydrogen bond between the two components. A hierarchy of hydrogen bond formation is observed in which the best donor in the system, the phenolic O-H group of paracetamol, is preferentially hydrogen bonded to the best acceptor, the basic nitrogen atom of the co-crystal former. The geometric aspects of the hydrogen bonds in co-crystals 1-3 are discussed in terms of their electrostatic and charge-transfer components.