Under the European Union's Digital Markets Act (DMA), six 'gatekeepers' (Alphabet, Amazon, Apple, ByteDance, Meta and Microsoft) have been designated in relation to 22 core platform services (CPS). The gatekeepers have until 6 March 2024 to propose to the European Commission how they will comply with their DMA obligations. The DMA gives flexibility to gatekeepers to achieve compliance by providing some guidance what can constitute compliance and non-compliance with the obligations. However, it does not provide compliance principles. These offer a standard of compliance-by-design, while offering flexibility to each gatekeeper to develop specific solutions tailored to each obligation and CPS. Compliance principles would also be easily observable elements helping to inform the Commission - the DMA's enforcer - about compliance. We propose five DMA compliance principles for gatekeepers to follow. These have been derived from the list of DMA obligations. The principles relate to access, fair conditions, information, choice and flexibility. Each principle would be accompanied by a second level of sub-principles based on the economics literature and case law. We recommend that gatekeepers implement the principles and that the Commission monitors whether gatekeepers follow the compliance principles. Gatekeepers, in their annual DMA compliance reports, should provide the Commission with methodologies, tests and other relevant documents as evidence of compliance in practice. Commission monitoring should include regular engagement with gatekeepers, third parties and consumers, before and after the implementation of the compliance solutions.