Programming :: Optimizing A Bash Script ?

I wrote a little Bash script which accepts two values -- sender address and recipient address -- and finds any instances of mail sent from sender to recipient in /var/log/maillog. The script works fine, but it seems to be very inefficient. I'm just wondering how I can optimize it.

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Again, it seems to work fine, but the script greps through /var/log/maillog three times -- first to find the sender; second to see if it's also going to the desired recipient; finally to view all instances of the message ID in the logs. This seems redundant and inefficient.