diff --git a/h3-quinn/src/datagram.rs b/h3-quinn/src/datagram.rs
index 807eb56e..7b993ce0 100644
--- a/h3-quinn/src/datagram.rs
+++ b/h3-quinn/src/datagram.rs
@@ -92,6 +92,9 @@ fn convert_h3_error_to_datagram_error(
         ConnectionErrorIncoming::ApplicationClose { error_code } => {
             h3_datagram::ConnectionErrorIncoming::ApplicationClose { error_code }
         }
+        ConnectionErrorIncoming::ConnectionClosed { error_code } => {
+            h3_datagram::ConnectionErrorIncoming::ConnectionClosed { error_code }
+        }
         ConnectionErrorIncoming::Timeout => h3_datagram::ConnectionErrorIncoming::Timeout,
         ConnectionErrorIncoming::InternalError(err) => {
             h3_datagram::ConnectionErrorIncoming::InternalError(err)
diff --git a/h3-quinn/src/lib.rs b/h3-quinn/src/lib.rs
index 4ac8a2af..7eaa264e 100644
--- a/h3-quinn/src/lib.rs
+++ b/h3-quinn/src/lib.rs
@@ -112,19 +112,44 @@ fn convert_connection_error(e: quinn::ConnectionError) -> h3::quic::ConnectionEr
                 error_code: application_close.error_code.into(),
             }
         }
+        quinn::ConnectionError::ConnectionClosed(connection_close) => {
+            ConnectionErrorIncoming::ConnectionClosed {
+                error_code: connection_close.error_code.into(),
+            }
+        }
         quinn::ConnectionError::TimedOut => ConnectionErrorIncoming::Timeout,
 
         error @ quinn::ConnectionError::VersionMismatch
         | error @ quinn::ConnectionError::Reset
         | error @ quinn::ConnectionError::LocallyClosed
         | error @ quinn::ConnectionError::CidsExhausted
-        | error @ quinn::ConnectionError::TransportError(_)
-        | error @ quinn::ConnectionError::ConnectionClosed(_) => {
+        | error @ quinn::ConnectionError::TransportError(_) => {
             ConnectionErrorIncoming::Undefined(Arc::new(error))
         }
     }
 }
 
+#[cfg(test)]
+mod tests {
+    use super::convert_connection_error;
+    use h3::quic::ConnectionErrorIncoming;
+    use quinn::{ConnectionClose, ConnectionError, TransportErrorCode};
+
+    #[test]
+    fn connection_closed_is_mapped_to_structured_variant() {
+        let error = ConnectionError::ConnectionClosed(ConnectionClose {
+            error_code: TransportErrorCode::NO_ERROR,
+            frame_type: None,
+            reason: Default::default(),
+        });
+
+        assert!(matches!(
+            convert_connection_error(error),
+            ConnectionErrorIncoming::ConnectionClosed { error_code: 0 }
+        ));
+    }
+}
+
 impl<B> quic::OpenStreams<B> for Connection
 where
     B: Buf,
diff --git a/h3/src/error/error.rs b/h3/src/error/error.rs
index 91313f9e..2ece1a78 100644
--- a/h3/src/error/error.rs
+++ b/h3/src/error/error.rs
@@ -1,5 +1,5 @@
 //! This is the public facing error types for the h3 crate
-use crate::quic::ConnectionErrorIncoming;
+use crate::quic::{ConnectionErrorIncoming, QUIC_NO_ERROR};
 
 use super::{codes::Code, internal_error::InternalConnectionError};
 
@@ -51,6 +51,11 @@ impl ConnectionError {
             {
                 true
             }
+            ConnectionError::Remote(ConnectionErrorIncoming::ConnectionClosed { error_code })
+                if *error_code == QUIC_NO_ERROR =>
+            {
+                true
+            }
             _ => false,
         }
     }
diff --git a/h3/src/quic.rs b/h3/src/quic.rs
index 923b46f8..21653870 100644
--- a/h3/src/quic.rs
+++ b/h3/src/quic.rs
@@ -13,6 +13,9 @@ use crate::error::Code;
 pub use crate::proto::stream::{InvalidStreamId, StreamId};
 pub use crate::stream::WriteBuf;
 
+/// QUIC transport close code indicating graceful shutdown.
+pub const QUIC_NO_ERROR: u64 = 0;
+
 /// Error type to communicate that the quic connection was closed
 ///
 /// This is used by to implement the quic abstraction traits
@@ -23,6 +26,11 @@ pub enum ConnectionErrorIncoming {
         /// http3 error code
         error_code: u64,
     },
+    /// QUIC connection was closed by peer
+    ConnectionClosed {
+        /// QUIC transport error code
+        error_code: u64,
+    },
     /// Quic connection timeout
     Timeout,
     /// This variant can be used to signal, that an internal error occurred within the trait implementations
@@ -42,6 +50,9 @@ impl Debug for ConnectionErrorIncoming {
                 let error_code = Code::from(*error_code);
                 write!(f, "ApplicationClose({})", error_code)
             }
+            Self::ConnectionClosed { error_code } => {
+                write!(f, "ConnectionClosed({:#x})", error_code)
+            }
             Self::Timeout => write!(f, "Timeout"),
             Self::InternalError(arg0) => f.debug_tuple("InternalError").field(arg0).finish(),
             Self::Undefined(arg0) => f.debug_tuple("Undefined").field(arg0).finish(),
@@ -100,6 +111,9 @@ impl Display for ConnectionErrorIncoming {
                 let error_code = Code::from(*error_code);
                 write!(f, "ApplicationClose: {}", error_code)
             }
+            ConnectionErrorIncoming::ConnectionClosed { error_code } => {
+                write!(f, "ConnectionClosed: {:#x}", error_code)
+            }
             ConnectionErrorIncoming::Timeout => write!(f, "Timeout"),
             ConnectionErrorIncoming::InternalError(error) => {
                 write!(