How to clear/reset syslog?

[joe at actionline.com]

The /var/log/syslog on my system got really large and cluttered up with a
new entry being added every minute for several days due to a "stuck"
printer (which I finally got corrected).  So I tried to restart the system
logger to clear out all the excess clutter and start over, but the command
to do that FAILS.  So is it okay to just delete the /var/log/syslog and
/var/log/message files to get a fresh start?

In addition to 'restart' (which FAILED), I also tried 'stop' and 'start'
(both of which work, although 'start' also returns a "FAILED" response
(which I don't understand).

In any case, if anyone would care to review the steps I've tried and the
results, I've posted a 65 line recap at the following link:

http://www.upquick.com/linux/restart.logger.txt

But my question is just this: Is there any problem or reason why I should
not just delete those two bloated log files?

Or, is there some other (better) way to clear out all the superfluous
excess in those log files?