Public Key Infrastructures (PKIs) with their trusted Certificate Authorities (CAs) provide the trust backbone for the Internet: CAs sign certificates which prove the identity of servers, applications, or users. To be trusted by operating systems and browsers, a CA has to undergo lengthy and costly validation processes. Alternatively, trusted CAs can cross-sign other CAs to extend their trust to them. In this paper, we systematically analyze the present and past state of cross-signing in the Web PKI. Our dataset (derived from passive TLS monitors and public CT logs) encompasses more than 7 years and 225 million certificates with 9.3 billion trust paths. We show benefits and risks of cross-signing. We discuss the difficulty of revoking trusted CA certificates where, worrisome, cross-signing can result in valid trust paths to remain after revocation; a problem for non-browser software that often blindly trusts all CA certificates and ignores revocations. However, cross-signing also enables fast bootstrapping of new CAs, e.g., Lets Encrypt, and achieves a non-disruptive user experience by providing backward compatibility. In this paper, we propose new rules and guidance for cross-signing to preserve its positive potential while mitigating its risks.