Those of us that work at Hispanic sites in the Southwest have shown unusual
innovation in disposing of tedious (roof tile fragments) that contribute
nothing to the analysis after weighing and recording.  After extensive discussions,
it is time to summarize. So far I have heard of the following  approaches:

1. saving everything (and quickly filling all storage space or paying
exorbitant fees for curation)

2. reburying the tile on site (and contaminating the site or confusing future
archaeologists)

3. hauling the tile away to a centralized culturally sterile area for
disposal (and carefully recording this fact for the benefit of future archaeologist)

4. abrogating responsibility and allowing your client to scatter them about
and use them for erosion control, pathways, or resale in the gift shop (as
smaller sherds).  The last option is the worst, in my opinion, as it reduces
artifacts to salable items.

So far, I have found #3 to be the best option for me, although I suppose
conditions vary at each site.