diff --git a/linkerd/http/upgrade/src/upgrade.rs b/linkerd/http/upgrade/src/upgrade.rs
index 14bbc6ffa1..5540266981 100644
--- a/linkerd/http/upgrade/src/upgrade.rs
+++ b/linkerd/http/upgrade/src/upgrade.rs
@@ -37,11 +37,6 @@ struct Http11UpgradeHalves {
     client: Http11Upgrade,
 }
 
-/// A marker type inserted into Extensions to signal it was an HTTP CONNECT
-/// request.
-#[derive(Debug)]
-pub struct HttpConnect;
-
 struct Inner {
     server: TryLock<Option<OnUpgrade>>,
     client: TryLock<Option<OnUpgrade>>,
diff --git a/linkerd/proxy/http/src/h1.rs b/linkerd/proxy/http/src/h1.rs
index b43dd1874a..b91a23a24a 100644
--- a/linkerd/proxy/http/src/h1.rs
+++ b/linkerd/proxy/http/src/h1.rs
@@ -6,10 +6,7 @@ use http::{
 };
 use linkerd_error::{Error, Result};
 use linkerd_http_box::BoxBody;
-use linkerd_http_upgrade::{
-    glue::HyperConnect,
-    upgrade::{Http11Upgrade, HttpConnect},
-};
+use linkerd_http_upgrade::{glue::HyperConnect, upgrade::Http11Upgrade};
 use linkerd_stack::MakeConnection;
 use std::{pin::Pin, time::Duration};
 use tracing::{debug, trace};
@@ -139,12 +136,6 @@ where
         Box::pin(async move {
             let mut rsp = rsp_fut.await?;
             if is_http_connect {
-                // Add an extension to indicate that this a response to a CONNECT request.
-                debug_assert!(
-                    upgrade.is_some(),
-                    "Upgrade extension must be set on CONNECT requests"
-                );
-                rsp.extensions_mut().insert(HttpConnect);
                 // Strip headers that may not be transmitted to the server, per RFC 9110:
                 //
                 // > A server MUST NOT send any `Transfer-Encoding` or `Content-Length` header
@@ -159,7 +150,7 @@ where
                 }
             }
 
-            if is_upgrade(&rsp) {
+            if is_upgrade(&rsp, is_http_connect) {
                 trace!("Client response is HTTP/1.1 upgrade");
                 if let Some(upgrade) = upgrade {
                     upgrade.insert_half(hyper::upgrade::on(&mut rsp))?;
@@ -174,36 +165,32 @@ where
 }
 
 /// Checks responses to determine if they are successful HTTP upgrades.
-fn is_upgrade<B>(res: &http::Response<B>) -> bool {
-    #[inline]
-    fn is_connect_success<B>(res: &http::Response<B>) -> bool {
-        res.extensions().get::<HttpConnect>().is_some() && res.status().is_success()
-    }
-
-    // Upgrades were introduced in HTTP/1.1
-    if res.version() != http::Version::HTTP_11 {
-        if is_connect_success(res) {
-            tracing::warn!(
-                "A successful response to a CONNECT request had an incorrect HTTP version \
-                (expected HTTP/1.1, got {:?})",
-                res.version()
-            );
+fn is_upgrade<B>(rsp: &http::Response<B>, is_http_connect: bool) -> bool {
+    use http::Version;
+
+    match rsp.version() {
+        Version::HTTP_11 => match rsp.status() {
+            // `101 Switching Protocols` indicates an upgrade.
+            http::StatusCode::SWITCHING_PROTOCOLS => true,
+            // CONNECT requests are complete if status code is 2xx.
+            status if is_http_connect && status.is_success() => true,
+            // Just a regular HTTP response...
+            _ => false,
+        },
+        version => {
+            // Upgrades are specific to HTTP/1.1. They are not included in HTTP/1.0, nor are they
+            // supported in HTTP/2. If this response is associated with any protocol version
+            // besides HTTP/1.1, it is not applicable to an upgrade.
+            if is_http_connect && rsp.status().is_success() {
+                tracing::warn!(
+                    "A successful response to a CONNECT request had an incorrect HTTP version \
+                    (expected HTTP/1.1, got {:?})",
+                    version
+                );
+            }
+            false
         }
-        return false;
     }
-
-    // 101 Switching Protocols
-    if res.status() == http::StatusCode::SWITCHING_PROTOCOLS {
-        return true;
-    }
-
-    // CONNECT requests are complete if status code is 2xx.
-    if is_connect_success(res) {
-        return true;
-    }
-
-    // Just a regular HTTP response...
-    false
 }
 
 /// Returns if the request target is in `absolute-form`.