diff --git a/src/error.rs b/src/error.rs
index 48917db970..2bbb166811 100644
--- a/src/error.rs
+++ b/src/error.rs
@@ -131,6 +131,9 @@ pub(super) enum User {
         feature = "ffi"
     ))]
     BodyWriteAborted,
+    /// User tried to send a connect request with a nonzero body
+    #[cfg(all(feature = "client", feature = "http2"))]
+    InvalidConnectWithBody,
     /// Error from future of user's Service.
     #[cfg(any(
         all(any(feature = "client", feature = "server"), feature = "http1"),
@@ -395,6 +398,11 @@ impl Error {
         Error::new_user(User::Body).with(cause)
     }
 
+    #[cfg(all(feature = "client", feature = "http2"))]
+    pub(super) fn new_user_invalid_connect() -> Error {
+        Error::new_user(User::InvalidConnectWithBody)
+    }
+
     #[cfg(all(any(feature = "client", feature = "server"), feature = "http1"))]
     pub(super) fn new_shutdown(cause: std::io::Error) -> Error {
         Error::new(Kind::Shutdown).with(cause)
@@ -492,6 +500,10 @@ impl Error {
                 feature = "ffi"
             ))]
             Kind::User(User::BodyWriteAborted) => "user body write aborted",
+            #[cfg(all(feature = "client", feature = "http2"))]
+            Kind::User(User::InvalidConnectWithBody) => {
+                "user sent CONNECT request with non-zero body"
+            }
             #[cfg(any(
                 all(any(feature = "client", feature = "server"), feature = "http1"),
                 all(feature = "server", feature = "http2")
diff --git a/src/proto/h2/client.rs b/src/proto/h2/client.rs
index 5e9641e408..faf36dde7f 100644
--- a/src/proto/h2/client.rs
+++ b/src/proto/h2/client.rs
@@ -673,9 +673,9 @@ where
                         && headers::content_length_parse_all(req.headers())
                             .map_or(false, |len| len != 0)
                     {
-                        warn!("h2 connect request with non-zero body not supported");
+                        debug!("h2 connect request with non-zero body not supported");
                         cb.send(Err(TrySendError {
-                            error: crate::Error::new_h2(h2::Reason::INTERNAL_ERROR.into()),
+                            error: crate::Error::new_user_invalid_connect(),
                             message: None,
                         }));
                         continue;