The PA-28 had departed Moorabbin at 1734 ESuT and was on climb to 9,000 ft tracking via Melbourne, Fentons Hill and Mangalore to Tocumwal. The pilot had initially been in Instrument Meteorological Conditions but broke out of cloud just prior to passing over Fentons Hill. The B737 had departed Melbourne for Brisbane at 1747 ESuT and was tracking via a Runway 27 DOSEL 3 standard instrument departure (SID). The crew requested, and were given, a climb at 300 kts in lieu of the compulsory 250 kts below 10,000 ft, and the aircraft passed close to Fentons Hill while tracking on the SID. The crew reported that they were in cloud initially and broke out just past Fentons Hill. The air traffic controller had both aircraft on his frequency and attempted to coordinate a shortened track for the PA-28. This request was denied due to the volume of traffic. Consequently, the controller had to radar monitor the climb of three previously departed aircraft past the PA-28. Track shortening on this particular route is normally available. Additionally, the controller had two aircraft arriving from Adelaide which required a combination of radar vectoring and vertical separation to ensure their safe and timely arrival. The arrival track from the west crosses over the departure track from runway 27. The traffic volume and complexity required significant concentration by the controller who did not notice that the B737 and the PA-28 were on converging tracks. Radar analysis indicates that the two aircraft came within 1.3 NM whilst at the same altitude with the B737 passing in front of the PA-28. Neither crew saw the other aircraft and were not aware of the conflict. There was a breakdown of separation standards. Findings 1. The crews of both aircraft were operating in accordance with air traffic control instructions. 2. The traffic volume and complexity were such as to result in a high workload situation. 3. The air traffic controller did not notice that the two aircraft were converging into conflict. 4. The two aircraft came within 1.3 NM with no vertical separation. Safety Action Airservices Australia have initiated changes to the Melbourne terminal area airspace that will remove the area of conflict involving the inbound tracks from the west. These changes will come into effect on 20 June 1996 and will significantly reduce the workload on approach/departures control.