diff --git a/src/proto/h2/client.rs b/src/proto/h2/client.rs
index 1570d2ee0a..b285574f47 100644
--- a/src/proto/h2/client.rs
+++ b/src/proto/h2/client.rs
@@ -108,7 +108,7 @@ where
                             }
                             let (head, body) = req.into_parts();
                             let mut req = ::http::Request::from_parts(head, ());
-                            super::strip_connection_headers(req.headers_mut());
+                            super::strip_connection_headers(req.headers_mut(), true);
                             if let Some(len) = body.content_length() {
                                 headers::set_content_length_if_missing(req.headers_mut(), len);
                             }
diff --git a/src/proto/h2/mod.rs b/src/proto/h2/mod.rs
index de877f0bc7..6620877210 100644
--- a/src/proto/h2/mod.rs
+++ b/src/proto/h2/mod.rs
@@ -15,15 +15,17 @@ mod server;
 pub(crate) use self::client::Client;
 pub(crate) use self::server::Server;
 
-fn strip_connection_headers(headers: &mut HeaderMap) {
+fn strip_connection_headers(headers: &mut HeaderMap, is_request: bool) {
     // List of connection headers from:
     // https://developer.mozilla.org/en-US/docs/Web/HTTP/Headers/Connection
+    //
+    // TE headers are allowed in HTTP/2 requests as long as the value is "trailers", so they're
+    // tested separately.
     let connection_headers = [
         HeaderName::from_lowercase(b"keep-alive").unwrap(),
         HeaderName::from_lowercase(b"proxy-connection").unwrap(),
         PROXY_AUTHENTICATE,
         PROXY_AUTHORIZATION,
-        TE,
         TRAILER,
         TRANSFER_ENCODING,
         UPGRADE,
@@ -35,6 +37,17 @@ fn strip_connection_headers(headers: &mut HeaderMap) {
         }
     }
 
+    if is_request {
+        if headers.get(TE).map(|te_header| te_header != "trailers").unwrap_or(false) {
+            warn!("TE headers not set to \"trailers\" are illegal in HTTP/2 requests");
+            headers.remove(TE);
+        }
+    } else {
+        if headers.remove(TE).is_some() {
+            warn!("TE headers illegal in HTTP/2 responses");
+        }
+    }
+
     if let Some(header) = headers.remove(CONNECTION) {
         warn!(
             "Connection header illegal in HTTP/2: {}",
diff --git a/src/proto/h2/server.rs b/src/proto/h2/server.rs
index d78d4a254e..1ded63b33e 100644
--- a/src/proto/h2/server.rs
+++ b/src/proto/h2/server.rs
@@ -192,7 +192,7 @@ where
 
                     let (head, body) = res.into_parts();
                     let mut res = ::http::Response::from_parts(head, ());
-                    super::strip_connection_headers(res.headers_mut());
+                    super::strip_connection_headers(res.headers_mut(), false);
                     if let Some(len) = body.content_length() {
                         headers::set_content_length_if_missing(res.headers_mut(), len);
                     }
diff --git a/tests/integration.rs b/tests/integration.rs
index e593284bba..9e7450b685 100644
--- a/tests/integration.rs
+++ b/tests/integration.rs
@@ -184,6 +184,30 @@ t! {
             ;
 }
 
+t! {
+    get_allow_te_trailers_header,
+    client:
+        request:
+            uri: "/",
+            headers: {
+                // http2 strips connection headers other than TE "trailers"
+                "te" => "trailers",
+            },
+            ;
+        response:
+            status: 200,
+            ;
+    server:
+        request:
+            uri: "/",
+            headers: {
+                "te" => "trailers",
+            },
+            ;
+        response:
+            ;
+}
+
 t! {
     get_body_chunked,
     client: