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Fingerprinting schemes deter people from illegally redistributing digital data by enabling the original merchant of the data to identify the original buyer of a redistributed copy. So-called traitor-tracing schemes have the same goal for keys used to decrypt information that is broadcast in encrypted form. Recently, asymmetric fingerprinting and traitor-tracing schemes were introduced. Here, only the buyer knows the fingerprinted copy after a sale, and if the merchant finds this copy somewhere, he obtains a proof that he found the copy of this particular buyer. This gives both parties security in disputes. First constructions showed the validity of the concept. However, these constructions did not yet achieve much security against collusions, in contrast to known symmetric schemes. This paper presents asymmetric constructions without this restriction.