Advances in information technology, and its use in research, are increasing both the need for anonymized data and the risks of poor anonymization. Previous work presented a new privacy metric, δ-presence, that clearly links the quality of anonymization to the risk posed by inadequate anonymization. It was shown that existing anonymization techniques are inappropriate for situations where δ-presence is a good metric (specifically, where knowing an individual is in the database poses a privacy risk). This article addresses a practical problem with previous work, extending to situations where the data anonymizer is not assumed to have complete world knowledge. The algorithms are evaluated in the context of a real-world scenario, demonstrating practical applicability of the approach.