PCI DSS v4.0.1 — Requirement 9.4.6
Hard-copy materials with cardholder data are destroyed when no longer needed for business or legal reasons, as follows: materials are cross-cut shredded, incinerated, or pulped so that cardholder data cannot be reconstructed; materials are stored in secure storage containers prior to destruction.
This is the hard-copy requirement, and it is unusually prescriptive for PCI — it names the acceptable methods rather than describing an outcome. Quoted here from the Council's own published self-assessment questionnaire.