diff --git a/http2/ascii.go b/http2/ascii.go
new file mode 100644
index 0000000..0c58d72
--- /dev/null
+++ b/http2/ascii.go
@@ -0,0 +1,49 @@
+// Copyright 2021 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package http2
+
+import "strings"
+
+// asciiEqualFold is strings.EqualFold, ASCII only. It reports whether s and t
+// are equal, ASCII-case-insensitively.
+func asciiEqualFold(s, t string) bool {
+	if len(s) != len(t) {
+		return false
+	}
+	for i := 0; i < len(s); i++ {
+		if lower(s[i]) != lower(t[i]) {
+			return false
+		}
+	}
+	return true
+}
+
+// lower returns the ASCII lowercase version of b.
+func lower(b byte) byte {
+	if 'A' <= b && b <= 'Z' {
+		return b + ('a' - 'A')
+	}
+	return b
+}
+
+// isASCIIPrint returns whether s is ASCII and printable according to
+// https://tools.ietf.org/html/rfc20#section-4.2.
+func isASCIIPrint(s string) bool {
+	for i := 0; i < len(s); i++ {
+		if s[i] < ' ' || s[i] > '~' {
+			return false
+		}
+	}
+	return true
+}
+
+// asciiToLower returns the lowercase version of s if s is ASCII and printable,
+// and whether or not it was.
+func asciiToLower(s string) (lower string, ok bool) {
+	if !isASCIIPrint(s) {
+		return "", false
+	}
+	return strings.ToLower(s), true
+}
diff --git a/http2/ascii_test.go b/http2/ascii_test.go
new file mode 100644
index 0000000..0c4e4ab
--- /dev/null
+++ b/http2/ascii_test.go
@@ -0,0 +1,95 @@
+// Copyright 2021 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package http2
+
+import "testing"
+
+func TestASCIIEqualFold(t *testing.T) {
+	var tests = []struct {
+		name string
+		a, b string
+		want bool
+	}{
+		{
+			name: "empty",
+			want: true,
+		},
+		{
+			name: "simple match",
+			a:    "CHUNKED",
+			b:    "chunked",
+			want: true,
+		},
+		{
+			name: "same string",
+			a:    "chunked",
+			b:    "chunked",
+			want: true,
+		},
+		{
+			name: "Unicode Kelvin symbol",
+			a:    "chunKed", // This "K" is 'KELVIN SIGN' (\u212A)
+			b:    "chunked",
+			want: false,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := asciiEqualFold(tt.a, tt.b); got != tt.want {
+				t.Errorf("AsciiEqualFold(%q,%q): got %v want %v", tt.a, tt.b, got, tt.want)
+			}
+		})
+	}
+}
+
+func TestIsASCIIPrint(t *testing.T) {
+	var tests = []struct {
+		name string
+		in   string
+		want bool
+	}{
+		{
+			name: "empty",
+			want: true,
+		},
+		{
+			name: "ASCII low",
+			in:   "This is a space: ' '",
+			want: true,
+		},
+		{
+			name: "ASCII high",
+			in:   "This is a tilde: '~'",
+			want: true,
+		},
+		{
+			name: "ASCII low non-print",
+			in:   "This is a unit separator: \x1F",
+			want: false,
+		},
+		{
+			name: "Ascii high non-print",
+			in:   "This is a Delete: \x7F",
+			want: false,
+		},
+		{
+			name: "Unicode letter",
+			in:   "Today it's 280K outside: it's freezing!", // This "K" is 'KELVIN SIGN' (\u212A)
+			want: false,
+		},
+		{
+			name: "Unicode emoji",
+			in:   "Gophers like 🧀",
+			want: false,
+		},
+	}
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := isASCIIPrint(tt.in); got != tt.want {
+				t.Errorf("IsASCIIPrint(%q): got %v want %v", tt.in, got, tt.want)
+			}
+		})
+	}
+}
diff --git a/http2/headermap.go b/http2/headermap.go
index c3ff3fa..9e12941 100644
--- a/http2/headermap.go
+++ b/http2/headermap.go
@@ -6,7 +6,6 @@
 
 import (
 	"net/http"
-	"strings"
 	"sync"
 )
 
@@ -79,10 +78,10 @@
 	}
 }
 
-func lowerHeader(v string) string {
+func lowerHeader(v string) (lower string, ascii bool) {
 	buildCommonHeaderMapsOnce()
 	if s, ok := commonLowerHeader[v]; ok {
-		return s
+		return s, true
 	}
-	return strings.ToLower(v)
+	return asciiToLower(v)
 }
diff --git a/http2/server.go b/http2/server.go
index 5ad3a2d..09bc705 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -2783,8 +2783,12 @@
 		// but PUSH_PROMISE requests cannot have a body.
 		// http://tools.ietf.org/html/rfc7540#section-8.2
 		// Also disallow Host, since the promised URL must be absolute.
-		switch strings.ToLower(k) {
-		case "content-length", "content-encoding", "trailer", "te", "expect", "host":
+		if asciiEqualFold(k, "content-length") ||
+			asciiEqualFold(k, "content-encoding") ||
+			asciiEqualFold(k, "trailer") ||
+			asciiEqualFold(k, "te") ||
+			asciiEqualFold(k, "expect") ||
+			asciiEqualFold(k, "host") {
 			return fmt.Errorf("promised request headers cannot include %q", k)
 		}
 	}
diff --git a/http2/transport.go b/http2/transport.go
index f89369e..7bd4b9c 100644
--- a/http2/transport.go
+++ b/http2/transport.go
@@ -995,7 +995,7 @@
 	if vv := req.Header["Transfer-Encoding"]; len(vv) > 0 && (len(vv) > 1 || vv[0] != "" && vv[0] != "chunked") {
 		return fmt.Errorf("http2: invalid Transfer-Encoding request header: %q", vv)
 	}
-	if vv := req.Header["Connection"]; len(vv) > 0 && (len(vv) > 1 || vv[0] != "" && !strings.EqualFold(vv[0], "close") && !strings.EqualFold(vv[0], "keep-alive")) {
+	if vv := req.Header["Connection"]; len(vv) > 0 && (len(vv) > 1 || vv[0] != "" && !asciiEqualFold(vv[0], "close") && !asciiEqualFold(vv[0], "keep-alive")) {
 		return fmt.Errorf("http2: invalid Connection request header: %q", vv)
 	}
 	return nil
@@ -1521,19 +1521,21 @@
 
 		var didUA bool
 		for k, vv := range req.Header {
-			if strings.EqualFold(k, "host") || strings.EqualFold(k, "content-length") {
+			if asciiEqualFold(k, "host") || asciiEqualFold(k, "content-length") {
 				// Host is :authority, already sent.
 				// Content-Length is automatic, set below.
 				continue
-			} else if strings.EqualFold(k, "connection") || strings.EqualFold(k, "proxy-connection") ||
-				strings.EqualFold(k, "transfer-encoding") || strings.EqualFold(k, "upgrade") ||
-				strings.EqualFold(k, "keep-alive") {
+			} else if asciiEqualFold(k, "connection") ||
+				asciiEqualFold(k, "proxy-connection") ||
+				asciiEqualFold(k, "transfer-encoding") ||
+				asciiEqualFold(k, "upgrade") ||
+				asciiEqualFold(k, "keep-alive") {
 				// Per 8.1.2.2 Connection-Specific Header
 				// Fields, don't send connection-specific
 				// fields. We have already checked if any
 				// are error-worthy so just ignore the rest.
 				continue
-			} else if strings.EqualFold(k, "user-agent") {
+			} else if asciiEqualFold(k, "user-agent") {
 				// Match Go's http1 behavior: at most one
 				// User-Agent. If set to nil or empty string,
 				// then omit it. Otherwise if not mentioned,
@@ -1546,7 +1548,7 @@
 				if vv[0] == "" {
 					continue
 				}
-			} else if strings.EqualFold(k, "cookie") {
+			} else if asciiEqualFold(k, "cookie") {
 				// Per 8.1.2.5 To allow for better compression efficiency, the
 				// Cookie header field MAY be split into separate header fields,
 				// each with one or more cookie-pairs.
@@ -1605,7 +1607,12 @@
 
 	// Header list size is ok. Write the headers.
 	enumerateHeaders(func(name, value string) {
-		name = strings.ToLower(name)
+		name, ascii := asciiToLower(name)
+		if !ascii {
+			// Skip writing invalid headers. Per RFC 7540, Section 8.1.2, header
+			// field names have to be ASCII characters (just as in HTTP/1.x).
+			return
+		}
 		cc.writeHeader(name, value)
 		if traceHeaders {
 			traceWroteHeaderField(trace, name, value)
@@ -1653,9 +1660,14 @@
 	}
 
 	for k, vv := range req.Trailer {
+		lowKey, ascii := asciiToLower(k)
+		if !ascii {
+			// Skip writing invalid headers. Per RFC 7540, Section 8.1.2, header
+			// field names have to be ASCII characters (just as in HTTP/1.x).
+			continue
+		}
 		// Transfer-Encoding, etc.. have already been filtered at the
 		// start of RoundTrip
-		lowKey := strings.ToLower(k)
 		for _, v := range vv {
 			cc.writeHeader(lowKey, v)
 		}
diff --git a/http2/transport_test.go b/http2/transport_test.go
index 7b13928..750813b 100644
--- a/http2/transport_test.go
+++ b/http2/transport_test.go
@@ -2219,6 +2219,11 @@
 		},
 		{
 			key:   "Transfer-Encoding",
+			value: []string{"chunKed"}, // Kelvin sign
+			want:  "ERROR: http2: invalid Transfer-Encoding request header: [\"chunKed\"]",
+		},
+		{
+			key:   "Transfer-Encoding",
 			value: []string{"chunked", "other"},
 			want:  "ERROR: http2: invalid Transfer-Encoding request header: [\"chunked\" \"other\"]",
 		},
diff --git a/http2/write.go b/http2/write.go
index 3849bc2..33f6139 100644
--- a/http2/write.go
+++ b/http2/write.go
@@ -341,7 +341,12 @@
 	}
 	for _, k := range keys {
 		vv := h[k]
-		k = lowerHeader(k)
+		k, ascii := lowerHeader(k)
+		if !ascii {
+			// Skip writing invalid headers. Per RFC 7540, Section 8.1.2, header
+			// field names have to be ASCII characters (just as in HTTP/1.x).
+			continue
+		}
 		if !validWireHeaderFieldName(k) {
 			// Skip it as backup paranoia. Per
 			// golang.org/issue/14048, these should