It may be a solution, but I would like to add an obsevation, something I saw during X-ray inspection:
The corner balls which shorted in our case were the same balls which on good reworked BGA's had an odd shape- mainly like a Pisa Tower.
I think that during cooling an "equilibrium" was achieved between the more and the less expanded side of the solder joints. It was interesting to see that the deviation grew from the middle of the row towards the end. And it was not a screen image error, as it often happens. Putting the corner balls in the middle of the screen, we saw it clearly.
If the balls were High temp balls, in our case I think that without melting, this situation would have led to opens, depending of course on the quantity of solder paste .
.....????
Gaby

To My E-Mail Address wrote:

To the assembly people, just a thought.
It seems that the total flexing of BGA due to size and mismatched CTEs is a
given. WHY not try high temp balls that do not collapse as much and hence
reduced or no bridging. It may cost a bit more but I am sure it is worth
considering what you pay for reworking those BGAs. I am sure TI will be
willing to work with you guys because that may be quick fix, without doing
extensive studies on finding materials and/or narrowing process window too
much.
Steve may be you can try this at the rework level. Reball the BGAs using
high temp balls.
Just an engineer thinking.
Rush