I am assuming I need to switch drivers, and I am assuming further I will want to try what I see under the Synaptic Package Manager: FGLRX. It says there in the textual clarification:
This package provides display drivers and hardware accelerated OpenGL
for X.Org. For 3D acceleration to work, you will need to
compile the fglrx kernel module for your kernel: see the fglrx-modules-dkms
package. Note that the driver will work without the kernel module, but 3D
acceleration will be disabled.
I am somewhat hesitant because, when I first installed LMDE over the weekend, I tried to compile and run a driver I downloaded from the AMD Radeon site, but I ended up trashing my system badly enough that it seemed far easier to reinstall LMDE from scratch than to try to rescue a mess with a panicked kernel. :-)
But the above notwithstanding, I will try the compile if someone would be kind enough to sell me a clue on how to get started doing that. :-)
By the way (probably unrelated), when I open a Terminal and type "compiz", my session resets abruptly and I am back at the login prompt. Even typing "compiz --help" does that!