The TCP Accelerated Open (TAO) is designed to cut down the number of packets needed to establish connection with a host, with the original 3-Way Handshake proving to be more complicated than what was needed.
There are a number of new options that T/TCP introduces. These options allow the establishment of a connection with a host using the TAO. T/TCP uses a 32-bit incarnation number, called a connection count (CC). This option is carried in the options part of a T/TCP segment, figure 4.1. A distinct CC value is assigned to each direction of an open connection. Incremental CC values are assigned to each connection that a host establishes, either actively or passively.
The 3-Way Handshake is bypassed using the CC value. Each server host caches in memory, or a file, the last valid CC value it received from each different client host. This CC value is sent with the initial SYN segment to the server. If the initial CC value for a particular client host is larger than the corresponding cached value, the property of the CC's (the increasing numbers) ensures that the SYN segment is new and can be accepted immediately. If the CC number is less than the one currently held in cache, the normal 3-Way Handshake is executed. Thus the TAO is an optimisation, with the normal 3-Way Handshake as a fall back.