diff --git a/http2/server.go b/http2/server.go
index b7524ba..d2ba820 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -2415,7 +2415,11 @@
 			clen = strconv.Itoa(len(p))
 		}
 		_, hasContentType := rws.snapHeader["Content-Type"]
-		if !hasContentType && bodyAllowedForStatus(rws.status) && len(p) > 0 {
+		// If the Content-Encoding is non-blank, we shouldn't
+		// sniff the body. See Issue golang.org/issue/31753.
+		ce := rws.snapHeader.Get("Content-Encoding")
+		hasCE := len(ce) > 0
+		if !hasCE && !hasContentType && bodyAllowedForStatus(rws.status) && len(p) > 0 {
 			ctype = http.DetectContentType(p)
 		}
 		var date string
diff --git a/http2/server_test.go b/http2/server_test.go
index 0b77919..7115a3e 100644
--- a/http2/server_test.go
+++ b/http2/server_test.go
@@ -6,6 +6,8 @@
 
 import (
 	"bytes"
+	"compress/gzip"
+	"compress/zlib"
 	"context"
 	"crypto/tls"
 	"errors"
@@ -3966,3 +3968,97 @@
 		t.Errorf("Read = %v, %v; want 0, non-nil", n, err)
 	}
 }
+
+// Issue 31753: don't sniff when Content-Encoding is set
+func TestContentEncodingNoSniffing(t *testing.T) {
+	type resp struct {
+		name string
+		body []byte
+		// setting Content-Encoding as an interface instead of a string
+		// directly, so as to differentiate between 3 states:
+		//    unset, empty string "" and set string "foo/bar".
+		contentEncoding interface{}
+		wantContentType string
+	}
+
+	resps := []*resp{
+		{
+			name:            "gzip content-encoding, gzipped", // don't sniff.
+			contentEncoding: "application/gzip",
+			wantContentType: "",
+			body: func() []byte {
+				buf := new(bytes.Buffer)
+				gzw := gzip.NewWriter(buf)
+				gzw.Write([]byte("doctype html><p>Hello</p>"))
+				gzw.Close()
+				return buf.Bytes()
+			}(),
+		},
+		{
+			name:            "zlib content-encoding, zlibbed", // don't sniff.
+			contentEncoding: "application/zlib",
+			wantContentType: "",
+			body: func() []byte {
+				buf := new(bytes.Buffer)
+				zw := zlib.NewWriter(buf)
+				zw.Write([]byte("doctype html><p>Hello</p>"))
+				zw.Close()
+				return buf.Bytes()
+			}(),
+		},
+		{
+			name:            "no content-encoding", // must sniff.
+			wantContentType: "application/x-gzip",
+			body: func() []byte {
+				buf := new(bytes.Buffer)
+				gzw := gzip.NewWriter(buf)
+				gzw.Write([]byte("doctype html><p>Hello</p>"))
+				gzw.Close()
+				return buf.Bytes()
+			}(),
+		},
+		{
+			name:            "phony content-encoding", // don't sniff.
+			contentEncoding: "foo/bar",
+			body:            []byte("doctype html><p>Hello</p>"),
+		},
+		{
+			name:            "empty but set content-encoding",
+			contentEncoding: "",
+			wantContentType: "audio/mpeg",
+			body:            []byte("ID3"),
+		},
+	}
+
+	tr := &Transport{TLSClientConfig: tlsConfigInsecure}
+	defer tr.CloseIdleConnections()
+
+	for _, tt := range resps {
+		t.Run(tt.name, func(t *testing.T) {
+			st := newServerTester(t, func(w http.ResponseWriter, r *http.Request) {
+				if tt.contentEncoding != nil {
+					w.Header().Set("Content-Encoding", tt.contentEncoding.(string))
+				}
+				w.Write(tt.body)
+			}, optOnlyServer)
+			defer st.Close()
+
+			req, _ := http.NewRequest("GET", st.ts.URL, nil)
+			res, err := tr.RoundTrip(req)
+			if err != nil {
+				t.Fatalf("Failed to fetch URL: %v", err)
+			}
+			defer res.Body.Close()
+			if g, w := res.Header.Get("Content-Encoding"), tt.contentEncoding; g != w {
+				if w != nil { // The case where contentEncoding was set explicitly.
+					t.Errorf("Content-Encoding mismatch\n\tgot:  %q\n\twant: %q", g, w)
+				} else if g != "" { // "" should be the equivalent when the contentEncoding is unset.
+					t.Errorf("Unexpected Content-Encoding %q", g)
+				}
+			}
+			if g, w := res.Header.Get("Content-Type"), tt.wantContentType; g != w {
+				t.Errorf("Content-Type mismatch\n\tgot:  %q\n\twant: %q", g, w)
+			}
+		})
+	}
+}