Option 1 seemed to be the most appealing. I began to scrape and discovered another layer of flooring, glued to the subfloor:
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEigebnU-IRCydHnd0nkRijOrFIZb45nfR93tbpifHai1lcn3GtTQq8gSZmqVik2DkE36x3XwW6UojmfF8NL5fDgsbYXm4NtH3xDkTiZjSaYrOwV_Q891t2l-uX9U7snt0CYwxReaC_4Yg/s320/ughmoretile.jpg)
This gave me pause, since ripping up even this little patch had taken hours. The floor was shaky. The more I read about tile, the more I discovered that the substrate (surface upon which the tile is installed) had to be especially sturdy. I really wanted to install travertine, a natural stone, which is even more fragile than ceramic tile and required even a sturdier subfloor. Also, it occurred to me that some sort of structural defect was causing the dip, and it must be dealt with. I cringed as a realized the only option was option 3, ripping everything out and starting from scratch.
To work around this, used a floor jack in the basement and a 4x4 post to jack the planks up off the joists. It was hard work. Three days, and a lot of blood and sweat later:
Note, you can actually see the dip in this picture on the fourth joist from the bottom of the picture.
After that, I wanted to make sure that these joists were not going to flex at all under the weight of the travertine I planned to install. I bought 12' long 2x6s to attach to and strengthen the existing joitss (called sistering, or buddy studding). I used 3/8" diameter bolts on either side of the joist, as well as 6 3 1/2" length decking screws, and liquid nails adhesive to attach the 'sisters' to the existing joists.
Incidentally, I found out that the dip was caused by a joist which had cracked, and the crack hidden with paint. As it turned out, the joist was cracked almost all the way through, and it was the subfloor that held the joist up, instead of vice versa.
I then installed 3/4" CDX plywood on top of the joists: