My St. Augustine yard really got healthy when I moved to strict organic methods and did three simple things; first I watered it deeply once a week so it would grow deeper roots, second I made my husband stop mowing it down to the ground and set the mower higher with a mulching mower and last I began adding cornmeal to the fertilizer application twice a year. It grew in more thick and lush and is still that way today.
Another thing this did was improve the health of the 50 year old ash tree in the yard. A great side benefit since it's huge and would be expensive to either take down or replace.
Bare spots react well to compost and a light mulch cover. Spare spots just need compost. Good luck with your yard!