Parallelization of KSPSolve() in multidimensions

[Rolf Kuiper]

Hi PETSc-Users,

when solving an implicit equation with KSPSolve() in 3D (communication  
with 7-point-stencil) I experienced the following:
Parallelization of the e.g. 64 x 64 x 64 domain on n cpus in the last  
direction (every cpu has a 64 x 64 x 64/n subdomain) leads to a  
parallel efficiency of approximately 90%, which is fine for us.
Parallelization of the e.g. 64 x 64 x 64 domain on n cpus in more than  
one direction (every cpu has e.g. a 64 x 64/sqrt(n) x 64/sqrt(n)  
subdomain) leads to a parallel efficiency of approximately 10%, which  
is absolutely unusable.

Is this behavior generally true for this kind of solver? If so, why?  
If not: What did I do wrong most presumably?
Has anybody made the same experience and/or could help me?

Thanks in advance,
Rolf