Proper configuration for database mirroring with witness and crossover cable for mirroring traffic

I am trying to setup a server with database mirroring in SQL 2005, but I need to have the mirroring traffic go over a crossover cable between the principal and the mirror.  DNS has an entry for the principal and mirror for these mirror interfaces so that they can see each other.

Principal - 3 NICs - Public, Private, Mirror
Public x.x.x.x, Private 10.10.1.101 (DB1.DOMAIN.LOCAL), Mirror 192.168.0.101 (DB1-DBM.DOMAIN.LOCAL)

Mirror - 3 NICs - Public, Private, Mirror
Public x.x.x.x, Private 10.10.1.102 (DB2.DOMAIN.LOCAL), Mirror 192.168.0.102 (DB2-DBM.DOMAIN.LOCAL)

Witness - 2 NICs - Public, Private
Public x.x.x.x, Private 10.10.1.103 (DBWITNESS.DOMAIN.LOCAL)



Do I need to add a third NIC to the witness to allow the witness to do its job?

If I do _not_ need a third NIC, what settings would I use when I "Configure Security" in the Mirroring setup to ensure that the witness will do it's job?  It seems like if I use the DB1-DBM and DB2-DBM in the settings, the witness will never be able to communicate with them since it does not have access to the 192.168.0.x network.