\'10-23\' DNAzymes can be used to cleave any target RNA in a sequence-specific manner. For applications in vivo, they have to be stabilised against nucleolytic attack by the introduction of modified nucleotides without obstructing cleavage activity. In this study, we optimise the design of a DNAzyme targeting the 5\'-non-translated region of the human rhinovirus 14, a common cold virus, with regard to its kinetic properties and its stability against nucleases. We compare a large number of DNAzymes against the same target site that are stabilised by the use of a 3\'-3\'-inverted thymidine, phosphorothioate linkages, 2\'-O-methyl RNA and locked nucleic acids, respectively. Both cleavage activity and nuclease stability were significantly enhanced by optimisation of arm length and content of modified nucleotides. Furthermore, we introduced modified nucleotides into the catalytic core to enhance stability against endonucleolytic degradation without abolishing catalytic activity. Our findings enabled us to establish a design for DNAzymes containing nucleotide modifications both in the binding arms and in the catalytic core, yielding a species with up to 10-fold enhanced activity and significantly elevated stability against nucleolytic cleavage. When transferring the design to a DNAzyme against a different target, only a slight modification was necessary to retain activity.