diff --git a/quic/core/http/end_to_end_test.cc b/quic/core/http/end_to_end_test.cc
index 2bc4917..e5b30c1 100644
--- a/quic/core/http/end_to_end_test.cc
+++ b/quic/core/http/end_to_end_test.cc
@@ -4193,7 +4193,7 @@
 
   EXPECT_TRUE(client_->client()->WaitForCryptoHandshakeConfirmed());
   static_cast<QuicSpdySession*>(client_->client()->session())
-      ->SetMaxAllowedPushId(kMaxQuicStreamId);
+      ->SetMaxPushId(kMaxQuicStreamId);
 
   client_->SendSynchronousRequest("/foo");
 
diff --git a/quic/core/http/quic_receive_control_stream.cc b/quic/core/http/quic_receive_control_stream.cc
index f9fdef9..7e74025 100644
--- a/quic/core/http/quic_receive_control_stream.cc
+++ b/quic/core/http/quic_receive_control_stream.cc
@@ -49,7 +49,9 @@
       stream_->spdy_session()->debug_visitor()->OnMaxPushIdFrameReceived(frame);
     }
 
-    stream_->spdy_session()->SetMaxAllowedPushId(frame.push_id);
+    // TODO(b/124216424): Signal error if received push ID is smaller than a
+    // previously received value.
+    stream_->spdy_session()->OnMaxPushIdFrame(frame.push_id);
     return true;
   }
 
diff --git a/quic/core/http/quic_send_control_stream.cc b/quic/core/http/quic_send_control_stream.cc
index 0ea3d6a..64c306a 100644
--- a/quic/core/http/quic_send_control_stream.cc
+++ b/quic/core/http/quic_send_control_stream.cc
@@ -116,6 +116,7 @@
 }
 
 void QuicSendControlStream::SendMaxPushIdFrame(PushId max_push_id) {
+  DCHECK_EQ(Perspective::IS_CLIENT, session()->perspective());
   QuicConnection::ScopedPacketFlusher flusher(session()->connection());
   MaybeSendSettingsFrame();
 
diff --git a/quic/core/http/quic_send_control_stream.h b/quic/core/http/quic_send_control_stream.h
index 3771cdd..03bd1f7 100644
--- a/quic/core/http/quic_send_control_stream.h
+++ b/quic/core/http/quic_send_control_stream.h
@@ -40,7 +40,7 @@
   void MaybeSendSettingsFrame();
 
   // Send a MAX_PUSH_ID frame on this stream, and a SETTINGS frame beforehand if
-  // one has not been already sent.
+  // one has not been already sent.  Must only be called for a client.
   void SendMaxPushIdFrame(PushId max_push_id);
 
   // Send a PRIORITY_UPDATE frame on this stream, and a SETTINGS frame
diff --git a/quic/core/http/quic_spdy_client_session_test.cc b/quic/core/http/quic_spdy_client_session_test.cc
index 15a9736..da05a15 100644
--- a/quic/core/http/quic_spdy_client_session_test.cc
+++ b/quic/core/http/quic_spdy_client_session_test.cc
@@ -583,8 +583,10 @@
   // Initialize crypto before the client session will create a stream.
   CompleteCryptoHandshake();
 
-  session_->SetMaxAllowedPushId(GetNthServerInitiatedUnidirectionalStreamId(
-      connection_->transport_version(), 10));
+  if (VersionHasIetfQuicFrames(connection_->transport_version())) {
+    session_->SetMaxPushId(GetNthServerInitiatedUnidirectionalStreamId(
+        connection_->transport_version(), 10));
+  }
 
   MockQuicSpdyClientStream* stream = static_cast<MockQuicSpdyClientStream*>(
       session_->CreateOutgoingBidirectionalStream());
@@ -603,9 +605,9 @@
       session_.get(), std::make_unique<QuicSpdyClientStream>(
                           stream_id, session_.get(), BIDIRECTIONAL));
 
-  session_->SetMaxAllowedPushId(GetNthServerInitiatedUnidirectionalStreamId(
-      connection_->transport_version(), 10));
   if (VersionHasIetfQuicFrames(connection_->transport_version())) {
+    session_->SetMaxPushId(GetNthServerInitiatedUnidirectionalStreamId(
+        connection_->transport_version(), 10));
     // TODO(b/136295430) Use PushId to represent Push IDs instead of
     // QuicStreamId.
     EXPECT_CALL(
@@ -644,8 +646,10 @@
   // Initialize crypto before the client session will create a stream.
   CompleteCryptoHandshake();
 
-  session_->SetMaxAllowedPushId(GetNthServerInitiatedUnidirectionalStreamId(
-      connection_->transport_version(), 10));
+  if (VersionHasIetfQuicFrames(connection_->transport_version())) {
+    session_->SetMaxPushId(GetNthServerInitiatedUnidirectionalStreamId(
+        connection_->transport_version(), 10));
+  }
 
   MockQuicSpdyClientStream* stream = static_cast<MockQuicSpdyClientStream*>(
       session_->CreateOutgoingBidirectionalStream());
@@ -914,7 +918,9 @@
       session_.get(), std::make_unique<QuicSpdyClientStream>(
                           stream_id, session_.get(), BIDIRECTIONAL));
 
-  session_->SetMaxAllowedPushId(kMaxQuicStreamId);
+  if (VersionHasIetfQuicFrames(connection_->transport_version())) {
+    session_->SetMaxPushId(kMaxQuicStreamId);
+  }
 
   EXPECT_CALL(*connection_, OnStreamReset(_, QUIC_REFUSED_STREAM));
 
diff --git a/quic/core/http/quic_spdy_session.cc b/quic/core/http/quic_spdy_session.cc
index 2b1b457..52bd00e 100644
--- a/quic/core/http/quic_spdy_session.cc
+++ b/quic/core/http/quic_spdy_session.cc
@@ -398,7 +398,7 @@
       spdy_framer_visitor_(new SpdyFramerVisitor(this)),
       server_push_enabled_(true),
       ietf_server_push_enabled_(false),
-      max_allowed_push_id_(0),
+      max_push_id_(0),
       destruction_indicator_(123456789),
       debug_visitor_(nullptr),
       http3_goaway_received_(false),
@@ -1211,33 +1211,43 @@
   }
 }
 
-void QuicSpdySession::SetMaxAllowedPushId(QuicStreamId max_allowed_push_id) {
-  if (!VersionUsesHttp3(transport_version())) {
-    return;
-  }
+void QuicSpdySession::SetMaxPushId(QuicStreamId max_push_id) {
+  DCHECK(VersionUsesHttp3(transport_version()));
+  DCHECK_EQ(Perspective::IS_CLIENT, perspective());
+  DCHECK_GE(max_push_id, max_push_id_);
 
-  QuicStreamId old_max_allowed_push_id = max_allowed_push_id_;
-  max_allowed_push_id_ = max_allowed_push_id;
-  QUIC_DVLOG(1) << ENDPOINT
-                << "Setting max_allowed_push_id to:  " << max_allowed_push_id_
-                << " from: " << old_max_allowed_push_id;
+  QuicStreamId old_max_push_id = max_push_id_;
+  max_push_id_ = max_push_id;
+  QUIC_DVLOG(1) << "Setting max_push_id to:  " << max_push_id_
+                << " from: " << old_max_push_id;
 
-  if (perspective() == Perspective::IS_SERVER) {
-    if (max_allowed_push_id_ > old_max_allowed_push_id) {
-      OnCanCreateNewOutgoingStream(true);
-    }
-    return;
-  }
-
-  DCHECK(perspective() == Perspective::IS_CLIENT);
   if (OneRttKeysAvailable()) {
     SendMaxPushId();
   }
 }
 
+bool QuicSpdySession::OnMaxPushIdFrame(QuicStreamId max_push_id) {
+  DCHECK(VersionUsesHttp3(transport_version()));
+  DCHECK_EQ(Perspective::IS_SERVER, perspective());
+
+  QuicStreamId old_max_push_id = max_push_id_;
+  max_push_id_ = max_push_id;
+  QUIC_DVLOG(1) << "Setting max_push_id to:  " << max_push_id_
+                << " from: " << old_max_push_id;
+
+  if (max_push_id_ > old_max_push_id) {
+    OnCanCreateNewOutgoingStream(true);
+    return true;
+  }
+
+  // Equal value is not considered an error.
+  return max_push_id >= old_max_push_id;
+}
+
 void QuicSpdySession::SendMaxPushId() {
   DCHECK(VersionUsesHttp3(transport_version()));
-  send_control_stream_->SendMaxPushIdFrame(max_allowed_push_id_);
+  DCHECK_EQ(Perspective::IS_CLIENT, perspective());
+  send_control_stream_->SendMaxPushIdFrame(max_push_id_);
 }
 
 void QuicSpdySession::EnableServerPush() {
diff --git a/quic/core/http/quic_spdy_session.h b/quic/core/http/quic_spdy_session.h
index bd1438b..3fa2963 100644
--- a/quic/core/http/quic_spdy_session.h
+++ b/quic/core/http/quic_spdy_session.h
@@ -295,16 +295,30 @@
   // those streams are not initialized yet.
   void OnCanCreateNewOutgoingStream(bool unidirectional) override;
 
-  void SetMaxAllowedPushId(QuicStreamId max_allowed_push_id);
+  // Sets |max_push_id_| and sends a MAX_PUSH_ID frame.
+  // This method must only be called if protocol is IETF QUIC and perspective is
+  // client.  |max_push_id| must be greater than or equal to current
+  // |max_push_id_|.
+  void SetMaxPushId(QuicStreamId max_push_id);
 
-  QuicStreamId max_allowed_push_id() { return max_allowed_push_id_; }
+  // Sets |max_push_id_|.
+  // This method must only be called if protocol is IETF QUIC and perspective is
+  // server.  It must only be called if a MAX_PUSH_ID frame is received.
+  // Returns whether |max_push_id| is greater than or equal to current
+  // |max_push_id_|.
+  bool OnMaxPushIdFrame(QuicStreamId max_push_id);
+
+  // TODO(b/151451061): Change this API to distinguish between having received
+  // no MAX_PUSH_ID frame and one MAX_PUSH_ID frame with push ID 0.
+  // TODO(b/136295430): Use sequential PUSH IDs instead of stream IDs.
+  QuicStreamId max_allowed_push_id() { return max_push_id_; }
 
   // Enables server push.
   // Must only be called when using IETF QUIC, for which server push is disabled
   // by default.  Server push defaults to enabled and cannot be disabled for
   // Google QUIC.
   // Must only be called for a server.  A client can effectively disable push by
-  // never calling SetMaxAllowedPushId().
+  // never calling SetMaxPushId().
   void EnableServerPush();
 
   int32_t destruction_indicator() const { return destruction_indicator_; }
@@ -506,7 +520,7 @@
   // Defaults to false.
   bool ietf_server_push_enabled_;
 
-  QuicStreamId max_allowed_push_id_;
+  QuicStreamId max_push_id_;
 
   // An integer used for live check. The indicator is assigned a value in
   // constructor. As long as it is not the assigned value, that would indicate
diff --git a/quic/tools/quic_simple_server_session_test.cc b/quic/tools/quic_simple_server_session_test.cc
index b127cd6..f9c28a7 100644
--- a/quic/tools/quic_simple_server_session_test.cc
+++ b/quic/tools/quic_simple_server_session_test.cc
@@ -757,7 +757,7 @@
   MaybeConsumeHeadersStreamData();
   if (VersionUsesHttp3(transport_version())) {
     session_->EnableServerPush();
-    session_->SetMaxAllowedPushId(kMaxQuicStreamId);
+    session_->OnMaxPushIdFrame(kMaxQuicStreamId);
   }
   size_t num_resources = kMaxStreamsForTest + 5;
   PromisePushResources(num_resources);
@@ -771,7 +771,7 @@
   MaybeConsumeHeadersStreamData();
   if (VersionUsesHttp3(transport_version())) {
     session_->EnableServerPush();
-    session_->SetMaxAllowedPushId(kMaxQuicStreamId);
+    session_->OnMaxPushIdFrame(kMaxQuicStreamId);
   }
   size_t num_resources = kMaxStreamsForTest + 1;
   QuicByteCount data_frame_header_length = PromisePushResources(num_resources);
@@ -849,7 +849,7 @@
   MaybeConsumeHeadersStreamData();
   if (VersionUsesHttp3(transport_version())) {
     session_->EnableServerPush();
-    session_->SetMaxAllowedPushId(kMaxQuicStreamId);
+    session_->OnMaxPushIdFrame(kMaxQuicStreamId);
   }
 
   // Having two extra resources to be send later. One of them will be reset, so
@@ -937,7 +937,7 @@
   MaybeConsumeHeadersStreamData();
   if (VersionUsesHttp3(transport_version())) {
     session_->EnableServerPush();
-    session_->SetMaxAllowedPushId(kMaxQuicStreamId);
+    session_->OnMaxPushIdFrame(kMaxQuicStreamId);
   }
   size_t num_resources = kMaxStreamsForTest + 1;
   if (VersionHasIetfQuicFrames(transport_version())) {
diff --git a/quic/tools/quic_spdy_client_base.cc b/quic/tools/quic_spdy_client_base.cc
index 429b09d..b4d4382 100644
--- a/quic/tools/quic_spdy_client_base.cc
+++ b/quic/tools/quic_spdy_client_base.cc
@@ -70,8 +70,9 @@
   }
   client_session()->Initialize();
   client_session()->CryptoConnect();
-  if (max_allowed_push_id_ > 0) {
-    client_session()->SetMaxAllowedPushId(max_allowed_push_id_);
+  if (max_allowed_push_id_ > 0 &&
+      VersionUsesHttp3(client_session()->transport_version())) {
+    client_session()->SetMaxPushId(max_allowed_push_id_);
   }
 }
 
diff --git a/quic/tools/quic_spdy_client_base.h b/quic/tools/quic_spdy_client_base.h
index 4d1642e..c4381f7 100644
--- a/quic/tools/quic_spdy_client_base.h
+++ b/quic/tools/quic_spdy_client_base.h
@@ -139,6 +139,7 @@
   bool drop_response_body() const { return drop_response_body_; }
 
   // Set the max promise id for the client session.
+  // TODO(b/151641466): Rename this method.
   void SetMaxAllowedPushId(QuicStreamId max) { max_allowed_push_id_ = max; }
 
   // Disables the use of the QPACK dynamic table and of blocked streams.