diff --git a/tuic-client/src/error.rs b/tuic-client/src/error.rs
index ddbaad5..013466f 100644
--- a/tuic-client/src/error.rs
+++ b/tuic-client/src/error.rs
@@ -11,8 +11,6 @@ pub enum Error {
     #[error(transparent)]
     Connect(#[from] ConnectError),
     #[error(transparent)]
-    Connection(#[from] ConnectionError),
-    #[error(transparent)]
     Model(#[from] ModelError),
     #[error("load native certificates error: {0}")]
     LoadNativeCerts(IoError),
@@ -29,3 +27,9 @@ pub enum Error {
     #[error("invalid socks5 authentication")]
     InvalidSocks5Auth,
 }
+
+impl From<ConnectionError> for Error {
+    fn from(err: ConnectionError) -> Self {
+        Self::Io(IoError::from(err))
+    }
+}
diff --git a/tuic-server/src/connection/handle_stream.rs b/tuic-server/src/connection/handle_stream.rs
index 088147d..8c0a0a9 100644
--- a/tuic-server/src/connection/handle_stream.rs
+++ b/tuic-server/src/connection/handle_stream.rs
@@ -40,7 +40,7 @@ impl Connection {
 
             tokio::select! {
                 () = self.auth.clone() => {}
-                err = self.inner.closed() => return Err(Error::Connection(err)),
+                err = self.inner.closed() => return Err(Error::from(err)),
             };
 
             let same_pkt_src = matches!(task, Task::Packet(_))
@@ -101,7 +101,7 @@ impl Connection {
 
             tokio::select! {
                 () = self.auth.clone() => {}
-                err = self.inner.closed() => return Err(Error::Connection(err)),
+                err = self.inner.closed() => return Err(Error::from(err)),
             };
 
             Ok(task)
@@ -135,7 +135,7 @@ impl Connection {
 
             tokio::select! {
                 () = self.auth.clone() => {}
-                err = self.inner.closed() => return Err(Error::Connection(err)),
+                err = self.inner.closed() => return Err(Error::from(err)),
             };
 
             let same_pkt_src = matches!(task, Task::Packet(_))
diff --git a/tuic-server/src/connection/mod.rs b/tuic-server/src/connection/mod.rs
index 3abe1a1..fe083ce 100644
--- a/tuic-server/src/connection/mod.rs
+++ b/tuic-server/src/connection/mod.rs
@@ -103,7 +103,7 @@ impl Connection {
 
                     match handle_incoming.await {
                         Ok(()) => {}
-                        Err(err) if err.is_locally_closed() || err.is_timeout_closed() => {
+                        Err(err) if err.is_trivial() => {
                             log::debug!(
                                 "[{id:#010x}] [{addr}] [{user}] {err}",
                                 id = conn.id(),
@@ -118,13 +118,16 @@ impl Connection {
                     }
                 }
             }
-            Err(err) if err.is_locally_closed() || err.is_timeout_closed() => {
-                log::debug!("[{id:#010x}] [{addr}] [unauthenticated] {err}", id = 0);
+            Err(err) if err.is_trivial() => {
+                log::debug!(
+                    "[{id:#010x}] [{addr}] [unauthenticated] {err}",
+                    id = u32::MAX,
+                );
             }
             Err(err) => {
                 log::warn!(
-                    "[{id:#010x}] [{addr}] [unauthenticated] connection establishing error: {err}",
-                    id = usize::MAX,
+                    "[{id:#010x}] [{addr}] [unauthenticated] {err}",
+                    id = u32::MAX,
                 )
             }
         }
diff --git a/tuic-server/src/error.rs b/tuic-server/src/error.rs
index 663d8ef..dec4e35 100644
--- a/tuic-server/src/error.rs
+++ b/tuic-server/src/error.rs
@@ -13,8 +13,10 @@ pub enum Error {
     Rustls(#[from] RustlsError),
     #[error("invalid max idle time")]
     InvalidMaxIdleTime,
-    #[error(transparent)]
-    Connection(#[from] ConnectionError),
+    #[error("connection timed out")]
+    TimedOut,
+    #[error("connection locally closed")]
+    LocallyClosed,
     #[error(transparent)]
     Model(#[from] ModelError),
     #[error("duplicated authentication")]
@@ -34,11 +36,17 @@ pub enum Error {
 }
 
 impl Error {
-    pub fn is_locally_closed(&self) -> bool {
-        matches!(self, Self::Connection(ConnectionError::LocallyClosed))
-    }
-
-    pub fn is_timeout_closed(&self) -> bool {
-        matches!(self, Self::Connection(ConnectionError::TimedOut))
+    pub fn is_trivial(&self) -> bool {
+        matches!(self, Self::TimedOut | Self::LocallyClosed)
+    }
+}
+
+impl From<ConnectionError> for Error {
+    fn from(err: ConnectionError) -> Self {
+        match err {
+            ConnectionError::TimedOut => Self::TimedOut,
+            ConnectionError::LocallyClosed => Self::LocallyClosed,
+            _ => Self::Io(IoError::from(err)),
+        }
     }
 }