I faced a similar problem but with a 8 ft ceiling. I wanted to get away from the standard fluorescent fixture in my 30 year old house? You know the 4-bulb - 4ft by 2ft box. I started looking at all kinds on lights, including flush mount, hanging, etc. I ruled them out because of the way they looked and the amount of light I could get out of them, plus CFLs could not be used in confined fixtures. So I ordered a 2- t5 -3ft long fluorescent fixtures. It seems that everything in lights is measured in eights of an inch. So t5 is 5/8 of an inch (small tubes). But I had to build a heat shield between the ceiling and fixture because the manufacture did not (actually took it from a $10 fixture at HD, cut it to size and added it). The fixture grew in depth. Next I quickly learned how to do leaded glass so I made a separate leaded glass cover for each of the two fixtures. The T5 output gives light equal to a 4ft although it is 3ft and tiny. I mounted my leaded glass cover and it looks pretty cool, except it is still fluorescent and about the same depth as the old fixture. So I took the wood panels off the fur downs above the cabinets. I cut holes in the sheetrock, got a mirror and checked down each wire filled, pipe filled joist. I finally concluded that I can add recessed lights. So I called an electrician. He came out and said I could cut the holes and run the wires and he would send an electrician to check everything and make the final connections. So to get away from the 8ft ceiling problem I am doing recessed lights.
Incidentally during the process I went to a neighbor with the same issue, 8ft room height. She added a simple flush mount. It looks great. Often wish I did that. Would have saved a lot of time and money, but this light project has become my hobby :-) Lowes has very, very nice flush mounts in a 2 pack for $20 (a great deal for good looking lights).
Good Luck,
Bob

Here's what I recommend for the short ceiling fan.