diff --git a/irctest/server_tests/test_channel_operations.py b/irctest/server_tests/test_channel_operations.py
index f98abc2..f651454 100644
--- a/irctest/server_tests/test_channel_operations.py
+++ b/irctest/server_tests/test_channel_operations.py
@@ -214,7 +214,19 @@ class JoinTestCase(cases.BaseServerTestCase):
         m = self.getMessage(1)
         self.assertMessageEqual(m, command='TOPIC', params=['#chan', 'T0P1C'])
 
+    @cases.SpecificationSelector.requiredBySpecification('RFC2812')
+    def testTopicNonexistentChannel(self):
+        """RFC2812 specifies ERR_NOTONCHANNEL as the correct response to TOPIC
+        on a nonexistent channel. The modern spec prefers ERR_NOSUCHCHANNEL.
 
+        <https://tools.ietf.org/html/rfc2812#section-3.2.4>
+        <http://modern.ircdocs.horse/#topic-message>
+        """
+        self.connectClient('foo')
+        self.sendLine(1, 'TOPIC #chan')
+        m = self.getMessage(1)
+        # either 403 ERR_NOSUCHCHANNEL or 443 ERR_NOTONCHANNEL
+        self.assertIn(m.command, ('403', '443'))
 
     @cases.SpecificationSelector.requiredBySpecification('RFC1459', 'RFC2812')
     def testListEmpty(self):
@@ -306,6 +318,15 @@ class JoinTestCase(cases.BaseServerTestCase):
         self.assertMessageEqual(m, command='KICK',
                 params=['#chan', 'bar', 'bye'])
 
+    @cases.SpecificationSelector.requiredBySpecification('RFC2812')
+    def testKickNonexistentChannel(self):
+        """“Kick command [...] Numeric replies: [...] ERR_NOSUCHCHANNEL."""
+        self.connectClient('foo')
+        self.sendLine(1, 'KICK #chan nick')
+        m = self.getMessage(1)
+        # should return ERR_NOSUCHCHANNEL
+        self.assertMessageEqual(m, command='403')
+
     @cases.SpecificationSelector.requiredBySpecification('RFC2812')
     def testDoubleKickMessages(self):
         """“The server MUST NOT send KICK messages with multiple channels or
diff --git a/irctest/server_tests/test_messages.py b/irctest/server_tests/test_messages.py
new file mode 100644
index 0000000..d8e705d
--- /dev/null
+++ b/irctest/server_tests/test_messages.py
@@ -0,0 +1,65 @@
+"""
+Section 3.2 of RFC 2812
+<https://tools.ietf.org/html/rfc2812#section-3.3>
+"""
+
+from irctest import cases
+from irctest import client_mock
+from irctest import runner
+from irctest.irc_utils import ambiguities
+from irctest.irc_utils.message_parser import Message
+
+class PrivmsgTestCase(cases.BaseServerTestCase):
+    @cases.SpecificationSelector.requiredBySpecification('RFC1459', 'RFC2812')
+    def testPrivmsg(self):
+        """<https://tools.ietf.org/html/rfc2812#section-3.3.1>"""
+        self.connectClient('foo')
+        self.sendLine(1, 'JOIN #chan')
+        self.connectClient('bar')
+        self.sendLine(2, 'JOIN #chan')
+        self.sendLine(1, 'PRIVMSG #chan :hello there')
+        self.getMessages(1) # synchronize
+        pms = [msg for msg in self.getMessages(2) if msg.command == 'PRIVMSG']
+        self.assertEqual(len(pms), 1)
+        self.assertMessageEqual(
+            pms[0],
+            command='PRIVMSG',
+            params=['#chan', 'hello there']
+        )
+
+    @cases.SpecificationSelector.requiredBySpecification('RFC1459', 'RFC2812')
+    def testPrivmsgNonexistentChannel(self):
+        """<https://tools.ietf.org/html/rfc2812#section-3.3.1>"""
+        self.connectClient('foo')
+        self.sendLine(1, 'PRIVMSG #nonexistent :hello there')
+        msg = self.getMessage(1)
+        # ERR_NOSUCHNICK, ERR_NOSUCHCHANNEL, or ERR_CANNOTSENDTOCHAN
+        self.assertIn(msg.command, ('401', '403', '404'))
+
+class NoticeTestCase(cases.BaseServerTestCase):
+    @cases.SpecificationSelector.requiredBySpecification('RFC1459', 'RFC2812')
+    def testNotice(self):
+        """<https://tools.ietf.org/html/rfc2812#section-3.3.2>"""
+        self.connectClient('foo')
+        self.sendLine(1, 'JOIN #chan')
+        self.connectClient('bar')
+        self.sendLine(2, 'JOIN #chan')
+        self.sendLine(1, 'NOTICE #chan :hello there')
+        self.getMessages(1) # synchronize
+        notices = [msg for msg in self.getMessages(2) if msg.command == 'NOTICE']
+        self.assertEqual(len(notices), 1)
+        self.assertMessageEqual(
+            notices[0],
+            command='NOTICE',
+            params=['#chan', 'hello there']
+        )
+
+    @cases.SpecificationSelector.requiredBySpecification('RFC1459', 'RFC2812')
+    def testNoticeNonexistentChannel(self):
+        """
+        'automatic replies MUST NEVER be sent in response to a NOTICE message'
+        https://tools.ietf.org/html/rfc2812#section-3.3.2>
+        """
+        self.connectClient('foo')
+        self.sendLine(1, 'NOTICE #nonexistent :hello there')
+        self.assertEqual(self.getMessages(1), [])