diff --git a/header.go b/header.go
index a04f4f90f5..8dab12acbe 100644
--- a/header.go
+++ b/header.go
@@ -2053,6 +2053,20 @@ func (s *headerScanner) next() bool {
 		s.nextColon = -1
 	} else {
 		n = bytes.IndexByte(s.b, ':')
+
+		// There can't be a \n inside the header name, check for this.
+		x := bytes.IndexByte(s.b, '\n')
+		if x < 0 {
+			// A header name should always at some point be followed by a \n
+			// even if it's the one that terminates the header block.
+			s.err = errNeedMore
+			return false
+		}
+		if x < n {
+			// There was a \n before the :
+			s.err = errInvalidName
+			return false
+		}
 	}
 	if n < 0 {
 		s.err = errNeedMore
@@ -2085,6 +2099,9 @@ func (s *headerScanner) next() bool {
 		if n+1 >= len(s.b) {
 			break
 		}
+		if s.b[n+1] != ' ' && s.b[n+1] != '\t' {
+			break
+		}
 		d := bytes.IndexByte(s.b[n+1:], '\n')
 		if d <= 0 {
 			break
@@ -2195,11 +2212,19 @@ func normalizeHeaderValue(ov, ob []byte, headerLength int) (nv, nb []byte, nhl i
 	}
 	write := 0
 	shrunk := 0
+	lineStart := false
 	for read := 0; read < length; read++ {
 		c := ov[read]
 		if c == '\r' || c == '\n' {
 			shrunk++
+			if c == '\n' {
+				lineStart = true
+			}
 			continue
+		} else if lineStart && c == '\t' {
+			c = ' '
+		} else {
+			lineStart = false
 		}
 		nv[write] = c
 		write++
@@ -2267,6 +2292,7 @@ func AppendNormalizedHeaderKeyBytes(dst, key []byte) []byte {
 
 var (
 	errNeedMore    = errors.New("need more data: cannot find trailing lf")
+	errInvalidName = errors.New("invalid header name")
 	errSmallBuffer = errors.New("small read buffer. Increase ReadBufferSize")
 )
 
diff --git a/header_test.go b/header_test.go
index 6f3aa0fe1a..cec008f5fa 100644
--- a/header_test.go
+++ b/header_test.go
@@ -15,37 +15,43 @@ import (
 func TestResponseHeaderMultiLineValue(t *testing.T) {
 	s := "HTTP/1.1 200 OK\r\n" +
 		"EmptyValue1:\r\n" +
-		"Content-Type: foo/bar;\r\n\tnewline;\r\n another/newline\r\n" + // the '\t' will be kept, won't be removed
+		"Content-Type: foo/bar;\r\n\tnewline;\r\n another/newline\r\n" +
 		"Foo: Bar\r\n" +
 		"Multi-Line: one;\r\n two\r\n" +
-		"Values: v1;\r\n v2;\r\n v3; v4\r\n" +
+		"Values: v1;\r\n v2; v3;\r\n v4;\tv5\r\n" +
 		"\r\n"
-	expectContentType := "foo/bar;\tnewline; another/newline"
-	// net/http not only remove "\r\n" but also replace \t to space
-	expectNetHttpContentType := "foo/bar; newline; another/newline"
-	expectMultiLine := "one; two"
 	header := new(ResponseHeader)
-	_, err := header.parse([]byte(s))
-	if err != nil {
+	if _, err := header.parse([]byte(s)); err != nil {
 		t.Fatalf("parse headers with multi-line values failed, %s", err)
 	}
-	gotContentType := header.Peek("Content-Type")
-	if string(gotContentType) != expectContentType {
-		t.Fatalf("unexpected content-type: %q. Expecting %q", gotContentType, expectContentType)
-	}
-	gotMultiLine := header.Peek("Multi-Line")
-	if string(gotMultiLine) != expectMultiLine {
-		t.Fatalf("unexpected multi-line: %q. Expecting %q", gotMultiLine, expectMultiLine)
-	}
-	// ensure behave same as net/http
 	response, err := http.ReadResponse(bufio.NewReader(strings.NewReader(s)), nil)
 	if err != nil {
 		t.Fatalf("parse response using net/http failed, %s", err)
 	}
-	gotNetHttpContentType := response.Header.Get("Content-Type")
-	if gotNetHttpContentType != expectNetHttpContentType {
-		t.Fatalf("unexpected content-type (net/http): %q. Expecting %q",
-			gotNetHttpContentType, expectNetHttpContentType)
+
+	for name, vals := range response.Header {
+		got := string(header.Peek(name))
+		want := vals[0]
+
+		if got != want {
+			t.Errorf("unexpected %s got: %q want: %q", name, got, want)
+		}
+	}
+}
+
+func TestResponseHeaderMultiLineName(t *testing.T) {
+	s := "HTTP/1.1 200 OK\r\n" +
+		"Host: golang.org\r\n" +
+		"Gopher-New-\r\n" +
+		" Line: This is a header on multiple lines\r\n" +
+		"\r\n"
+	header := new(ResponseHeader)
+	if _, err := header.parse([]byte(s)); err != errInvalidName {
+		m := make(map[string]string)
+		header.VisitAll(func(key, value []byte) {
+			m[string(key)] = string(value)
+		})
+		t.Errorf("expected error, got %q (%v)", m, err)
 	}
 }