diff --git a/pc/media_session.cc b/pc/media_session.cc
index e703b44101..92fe80f3d1 100644
--- a/pc/media_session.cc
+++ b/pc/media_session.cc
@@ -684,8 +684,11 @@ static bool CreateContentOffer(
       if (extension_with_id.uri == extension.uri) {
         // TODO(crbug.com/1051821): Configure the extension direction from
         // the information in the media_description_options extension
-        // capability.
-        extensions.push_back(extension_with_id);
+        // capability. For now, do not include stopped extensions.
+        // See also crbug.com/webrtc/7477 about the general lack of direction.
+        if (extension.direction != RtpTransceiverDirection::kStopped) {
+          extensions.push_back(extension_with_id);
+        }
       }
     }
   }
diff --git a/pc/media_session_unittest.cc b/pc/media_session_unittest.cc
index 8f38f6a1b4..6dc6d76021 100644
--- a/pc/media_session_unittest.cc
+++ b/pc/media_session_unittest.cc
@@ -2018,7 +2018,7 @@ TEST_F(MediaSessionDescriptionFactoryTest,
 }
 
 TEST_F(MediaSessionDescriptionFactoryTest,
-       AppendsStoppedExtensionIfKnownAndPresentInTheOffer) {
+       AllowsStoppedExtensionsToBeRemovedFromSubsequentOffer) {
   MediaSessionOptions opts;
   AddMediaDescriptionOptions(MEDIA_TYPE_VIDEO, "video",
                              RtpTransceiverDirection::kSendRecv, kActive,
@@ -2043,8 +2043,7 @@ TEST_F(MediaSessionDescriptionFactoryTest,
       ElementsAre(Property(
           &ContentInfo::media_description,
           Pointee(Property(&MediaContentDescription::rtp_header_extensions,
-                           ElementsAre(Field(&RtpExtension::uri, "uri1"),
-                                       Field(&RtpExtension::uri, "uri2")))))));
+                           ElementsAre(Field(&RtpExtension::uri, "uri1")))))));
 }
 
 TEST_F(MediaSessionDescriptionFactoryTest,
diff --git a/pc/peer_connection_header_extension_unittest.cc b/pc/peer_connection_header_extension_unittest.cc
index 1a452b0a1f..9bbc32b7e0 100644
--- a/pc/peer_connection_header_extension_unittest.cc
+++ b/pc/peer_connection_header_extension_unittest.cc
@@ -229,6 +229,68 @@ TEST_P(PeerConnectionHeaderExtensionTest, NegotiatedExtensionsAreAccessible) {
                           Field(&RtpHeaderExtensionCapability::uri, "uri3")));
 }
 
+TEST_P(PeerConnectionHeaderExtensionTest, OfferedExtensionsArePerTransceiver) {
+  cricket::MediaType media_type;
+  SdpSemantics semantics;
+  std::tie(media_type, semantics) = GetParam();
+  if (semantics != SdpSemantics::kUnifiedPlan)
+    return;
+  std::unique_ptr<PeerConnectionWrapper> pc1 =
+      CreatePeerConnection(media_type, semantics);
+  auto transceiver1 = pc1->AddTransceiver(media_type);
+  auto modified_extensions = transceiver1->HeaderExtensionsToOffer();
+  modified_extensions[3].direction = RtpTransceiverDirection::kStopped;
+  transceiver1->SetOfferedRtpHeaderExtensions(modified_extensions);
+  auto transceiver2 = pc1->AddTransceiver(media_type);
+
+  auto session_description = pc1->CreateOffer();
+  EXPECT_THAT(session_description->description()
+                  ->contents()[0]
+                  .media_description()
+                  ->rtp_header_extensions(),
+              ElementsAre(Field(&RtpExtension::uri, "uri2"),
+                          Field(&RtpExtension::uri, "uri3")));
+  EXPECT_THAT(session_description->description()
+                  ->contents()[1]
+                  .media_description()
+                  ->rtp_header_extensions(),
+              ElementsAre(Field(&RtpExtension::uri, "uri2"),
+                          Field(&RtpExtension::uri, "uri3"),
+                          Field(&RtpExtension::uri, "uri4")));
+}
+
+TEST_P(PeerConnectionHeaderExtensionTest, RemovalAfterRenegotiation) {
+  cricket::MediaType media_type;
+  SdpSemantics semantics;
+  std::tie(media_type, semantics) = GetParam();
+  if (semantics != SdpSemantics::kUnifiedPlan)
+    return;
+  std::unique_ptr<PeerConnectionWrapper> pc1 =
+      CreatePeerConnection(media_type, semantics);
+  std::unique_ptr<PeerConnectionWrapper> pc2 =
+      CreatePeerConnection(media_type, semantics);
+  auto transceiver1 = pc1->AddTransceiver(media_type);
+
+  auto offer = pc1->CreateOfferAndSetAsLocal(
+      PeerConnectionInterface::RTCOfferAnswerOptions());
+  pc2->SetRemoteDescription(std::move(offer));
+  auto answer = pc2->CreateAnswerAndSetAsLocal(
+      PeerConnectionInterface::RTCOfferAnswerOptions());
+  pc1->SetRemoteDescription(std::move(answer));
+
+  auto modified_extensions = transceiver1->HeaderExtensionsToOffer();
+  modified_extensions[3].direction = RtpTransceiverDirection::kStopped;
+  modified_extensions[3].direction = RtpTransceiverDirection::kStopped;
+  transceiver1->SetOfferedRtpHeaderExtensions(modified_extensions);
+  auto session_description = pc1->CreateOffer();
+  EXPECT_THAT(session_description->description()
+                  ->contents()[0]
+                  .media_description()
+                  ->rtp_header_extensions(),
+              ElementsAre(Field(&RtpExtension::uri, "uri2"),
+                          Field(&RtpExtension::uri, "uri3")));
+}
+
 INSTANTIATE_TEST_SUITE_P(
     ,
     PeerConnectionHeaderExtensionTest,