We report the first thorough characterization of single crystals of CeCu2Si2. Measurements on these flux-grown crystals, which are not superconducting above 0.050 K, include ac susceptibility, resistivity, Hall effect, and specific heat. A review of other measurements is given, and the implications of our single-crystal data are discussed. Specifically, our data are consistent with superconductivity in CeCu2Si2 being destroyed by having too low a Kondo temperature, although TKondo is not found to be inversely proportional to as previously claimed. The entropy associated with the low-temperature specific-heat anomaly is found to be only 0.66R ln2, in contrast to the previous result of R ln2 for polycrystalline material. The lack of superconductivity in our single crystals does not appear to be due to poor stoichiometry to +5%, as proposed previously for single crystals grown by a Bridgman technique. The possibility of charge-density waves suppressing superconductivity in strain-free material is discussed, although no experimental verification is found. © 1983 The American Physical Society.