Preheating my splits on the firebox is a nice trick i learned on here, it gets them closer to their combustion temp and dries them out for quicker and more complete ignition when they are introduced to the coals. This is especially useful if they have gotten rained on, if its cold out... etc.
+1 for the small, healthy fire too. I have started using the smallest fire that will sustain the temp and refueling often.. Its a lot more work than just piling a bunch on there, but the results of the sweet blue smoke have been well worth it. Good luck figuring out your problem!