Hello,
Thanks everyone for the helpful tips in all of the posts.  I hope you can offer some to me.  My cat is about 13 years old, a female indoor cat.  Until about 5 years ago she traveled by plane about once per year-- we used sedation and she was small enough to carry on in a carrier.  She has always been a nervous cat.  We also moved twice during the past two years, and the two kids of the household left home for school and marriage.  
During the past two years, my cat has been pooping/eliminating outside of her litter box, in the living room near the piano (played by one of the kids).  Sometimes the poop has blood in it.  One time it was a small pool of blood.  The vet took x-rays and examined the cat while she was sedated, but found nothing wrong.  We tried to change her foods, in case she was allergic to a certain food or brand, but it did not work.  We found that after the vet gives her a cortizone shot she is better, but it does not last long.  A few months ago, the vet determined that she has Irritable Bowel Syndrome and that she should be treated like a human-- with antidepressants that will help her relax and then have normal bowel movements.  He said that it is actually common to prescribe these meds to cats, and that we would need to experiment with different doses and brands.  We started a tiny dose of prozac, and it worked for a few months.  But the bloody poops appeared at the piano again.  We increased the dosage, to no avail.  Now, she cries when she goes to the bathroom, and she is leaving bloody poops by the piano.
Anyone else heard of this type of behavior?   We would assume it was psychological, perhaps from changing houses or the kids leaving, but that does not explain the blood.  Anyone else using antidepressants to curb similar behavior?  Or seeing blood in their cat's stool without explanation?
I should add that we trust and respect our vet, he has been treating her all her life, including her declaw and spaying operations, and also treated other cats in our neighborhood.
Thanks in advance for any help.