Thanks for all your tips.  I will contact my CE to see if we have the latest
microcode update (we just installed the device in late February).  I ran the
test suggested as follows:

timex dd if=/dev/zero of=/dev/rmt1 bs=1024 count=1000

The result was real 21.06 seconds.  This falls way short of what I would
expect when the advertised sustained transfer rate is supposed to be
15MB/sec native (30MB/sec compressed).  The advertised transfer rates are
double what we had previously with the 3575 library, which is why we were
suprised by the poor performance.  We expected the 3584 to be faster, other
than the initial locate of the data on the tape.