Average movecount: 4 - 5
Average double moves: ~ 1
Over time using the beginners' tracing, one will realise that there are only 30 possible configurations that 5 and 6 can be in. Thus, one can memorise a trace circlet for each of these cases to substantially speed up the CP-recognition.
In 6 of the 30 cases, 5 and 6 are already friends. Therefore in these cases, the trace circlet is a simple circle. In another 8 cases, 5 and 6 are almost friends, i.e. 5 and 6 will become friends with a single U move or a single R move (neither of which tamper with CP so that is allowed) These cases are when 5 and 6 are in UFL-UFR, UBL-UBR, UFR-DFR or UBR-DBR. These cases also have a simple trace circlet that one can figure out on their own, even in the middle of inspection, without having to make swaps as required by the beginners' tracing.
The remaining 16 cases are shown above, where the circlet is mentioned with an identifiable name. The positions marked in light green are the ones where corners 5 and 6 are located in either permutation, and the orange line is the trace circlet. Depending on the permutation of corners 5 and 6, the direction of the circlet will be decided. Note, body diagonals have not been shown in the figures to keep them relatively clean-looking.
Here is the optimised version of CP tracing:
1. Locate corners 5 and 6.
2. Recall the trace circlet and its direction
3. Locate corner 4.
4. Follow the circlet in the appropriate direction and identify the next 2 corners
In case the DL corners are not solved (i.e. DBL corner is solved by definition, but the DFL corner is not), the DFL corner will be numbered as the corner currently stuck in the DFL position, and the rest of the tracing continues normally.
At the end of this exerise, one will end up one of 6 possible ordered pairs of numbers signifying the CP case. This can be used to determine which corners are to be swapped using the table given in the beginners' section.