Light aircraft pilot reported an NMAC with another light aircraft on visual approach to FFZ.

Narrative

I was cleared into the Class D by Falcon Tower when 11 miles southwest of the airport and told to make right hand entry for Runway 4L. Runway 4R is closed for construction. I was at 3;000 FT MSL and descending to pattern altitude of 2;400 when the Tower advised me of traffic to my right and behind me. I did not spot the traffic and reported [that] to the Tower. I was asked to IDENT two or three times. I was in contact with the Tower several times and given a clearance to land while about three miles from the airport. The Tower was in contact with two helicopters on the west side of the field at the same time and was having trouble determining which one was where. The next thing I see is a [low-wing light aircraft] below me and at my 10 o'clock. He had passed below me about 100 FT and was turning to base leg at that time. I was told to turn down wind and make it a long down wind. I was then told to make a 360 on down wind as I was about to exit the Falcon Class D airspace. I was then told to turn base. The rest of the landing sequence was without incident.