Postfix backup server accepting mail for invalid.userid@valid.domain

Hello all,

How can I configure my postfix backup mail server, which also relays
for the domain, to REJECT any mail if it is not a valid mailbox? My
primary rejects mail for invalid mailboxes fine, but the backup server
still relays if the domain is one of the valid domain names as
specified in "relay_domains = /usr/local/etc/postfix/relays.txt"
regardless of whether the userid/mailbox is valid or not.

Thank you for you help.

-Amir