Explicit Congestion Notification (ECN) is a mechanism by which network nodes can mark IP packets instead of dropping them to indicate incipient congestion to the endpoints. Receivers with an ECN-capable transport protocol feed back this information to the sender. ECN was originally specified for TCP in such a way that only one feedback signal can be transmitted per Round-Trip Time (RTT). More recently defined mechanisms like Congestion Exposure (ConEx), Data Center TCP (DCTCP), or Low Latency, Low Loss, and Scalable Throughput (L4S) need more accurate ECN feedback information whenever more than one marking is received in one RTT. This document updates the original ECN specification defined in RFC 3168 by specifying a scheme that provides more than one feedback signal per RTT in the TCP header, called More Accurate ECN (AccECN). Given TCP header space is scarce, it allocates a reserved header bit previously assigned to the ECN-nonce. It also overloads the two existing ECN flags in the TCP header. The resulting extra space is additionally exploited to feed back the IP-ECN field received during the TCP connection establishment. Supplementary feedback information can optionally be provided in two new TCP Option alternatives, which are never used on the TCP SYN. The document also specifies the treatment of this updated TCP wire protocol by middleboxes.