Qantas 10 was one of four south-east bound aircraft estimating overhead Curtin reporting point at approximately 0000 WST. Lauder Air 2 was north-west bound and estimating Curtin at approximately 0100 WST. Several other aircraft were also due to enter the airspace around Curtin during this period. Lauder Air 2 was maintaining FL350 (35,000 feet). Qantas 10 was maintaining FL310 and had requested FL370. The duty Air Traffic Controller (ATC) cleared Qantas 10 to climb to FL330, at Curtin, with an expectation that a clearance to FL370 would be available later. The complexity of the traffic situation required the duty ATC to co-ordinate traffic with Melbourne Sector and to make a number of calculations associated with the "time of passing" between Qantas 10 and other aircraft. During this process the ATC, incorrectly, wrote the "time of passing" between Qantas 10 and another aircraft on the Lauder Air 2 flight strip. The correct "time of passing" between Qantas 10 and Lauder Air 2 was 0029 but the duty ATC wrote 0047 on the Lauder Air flight strip. A "time of passing" of 0047 was also entered on Qantas 10's flight strip. Following advice from Melbourne, at 0026, that Qantas 10 would be accepted at FL370 the duty ATC checked the "time of passing" written on the flight strip (0047) to ensure that sufficient time for the climb was available, (ten minutes for the climb and ten minutes for the buffer), and cleared Qantas 10 to climb to FL370. As Qantas 10 commenced climbing the crew observed the lights of Lauder Air 2 directly ahead. Qantas 10 stopped its climb at FL340 and reported the situation to the duty ATC who then instructed Qantas 10 to descend again to FL330. Lauder Air 2 passed directly overhead and 1500 feet above Qantas 10. The investigation determined that the duty ATC, who was assessed as very experienced and competent, had also made other procedural errors during his time at the console. Evidence was available which indicated that the errors were probably the result of accumulated fatigue brought on by a lack of sleep and disrupted sleep patterns, a lack of adequate rest breaks over both the long and the short term and pressure caused by the additional tasks associated with his position as a Team Leader.