diff --git a/src/compress/gzip/gunzip.go b/src/compress/gzip/gunzip.go
index bc303898b3..8bd750bd8b 100644
--- a/src/compress/gzip/gunzip.go
+++ b/src/compress/gzip/gunzip.go
@@ -186,7 +186,11 @@ func (z *Reader) readHeader() (hdr Header, err error) {
 		return hdr, ErrHeader
 	}
 	flg := z.buf[3]
-	hdr.ModTime = time.Unix(int64(le.Uint32(z.buf[4:8])), 0)
+	if t := int64(le.Uint32(z.buf[4:8])); t > 0 {
+		// Section 2.3.1, the zero value for MTIME means that the
+		// modified time is not set.
+		hdr.ModTime = time.Unix(t, 0)
+	}
 	// z.buf[8] is XFL and is currently ignored.
 	hdr.OS = z.buf[9]
 	z.digest = crc32.ChecksumIEEE(z.buf[:10])
diff --git a/src/compress/gzip/gzip.go b/src/compress/gzip/gzip.go
index c70321970b..aafb442a66 100644
--- a/src/compress/gzip/gzip.go
+++ b/src/compress/gzip/gzip.go
@@ -10,6 +10,7 @@ import (
 	"fmt"
 	"hash/crc32"
 	"io"
+	"time"
 )
 
 // These constants are copied from the flate package, so that code that imports
@@ -143,10 +144,7 @@ func (z *Writer) Write(p []byte) (int, error) {
 	// Write the GZIP header lazily.
 	if !z.wroteHeader {
 		z.wroteHeader = true
-		z.buf[0] = gzipID1
-		z.buf[1] = gzipID2
-		z.buf[2] = gzipDeflate
-		z.buf[3] = 0
+		z.buf = [10]byte{0: gzipID1, 1: gzipID2, 2: gzipDeflate}
 		if z.Extra != nil {
 			z.buf[3] |= 0x04
 		}
@@ -156,13 +154,15 @@ func (z *Writer) Write(p []byte) (int, error) {
 		if z.Comment != "" {
 			z.buf[3] |= 0x10
 		}
-		le.PutUint32(z.buf[4:8], uint32(z.ModTime.Unix()))
+		if z.ModTime.After(time.Unix(0, 0)) {
+			// Section 2.3.1, the zero value for MTIME means that the
+			// modified time is not set.
+			le.PutUint32(z.buf[4:8], uint32(z.ModTime.Unix()))
+		}
 		if z.level == BestCompression {
 			z.buf[8] = 2
 		} else if z.level == BestSpeed {
 			z.buf[8] = 4
-		} else {
-			z.buf[8] = 0
 		}
 		z.buf[9] = z.OS
 		n, z.err = z.w.Write(z.buf[:10])
diff --git a/src/compress/gzip/gzip_test.go b/src/compress/gzip/gzip_test.go
index 09271b24e9..865c529f55 100644
--- a/src/compress/gzip/gzip_test.go
+++ b/src/compress/gzip/gzip_test.go
@@ -8,6 +8,7 @@ import (
 	"bufio"
 	"bytes"
 	"io/ioutil"
+	"reflect"
 	"testing"
 	"time"
 )
@@ -24,6 +25,9 @@ func TestEmpty(t *testing.T) {
 	if err != nil {
 		t.Fatalf("NewReader: %v", err)
 	}
+	if want := (Header{OS: 255}); !reflect.DeepEqual(r.Header, want) {
+		t.Errorf("Header mismatch:\ngot  %#v\nwant %#v", r.Header, want)
+	}
 	b, err := ioutil.ReadAll(r)
 	if err != nil {
 		t.Fatalf("ReadAll: %v", err)
diff --git a/src/compress/gzip/issue14937_test.go b/src/compress/gzip/issue14937_test.go
index 432ad16b1c..e76d47cc4e 100644
--- a/src/compress/gzip/issue14937_test.go
+++ b/src/compress/gzip/issue14937_test.go
@@ -7,7 +7,6 @@ import (
 	"runtime"
 	"strings"
 	"testing"
-	"time"
 )
 
 // Per golang.org/issue/14937, check that every .gz file
@@ -16,8 +15,12 @@ func TestGZIPFilesHaveZeroMTimes(t *testing.T) {
 	if testing.Short() && testenv.Builder() == "" {
 		t.Skip("skipping in short mode")
 	}
+	goroot, err := filepath.EvalSymlinks(runtime.GOROOT())
+	if err != nil {
+		t.Fatal("error evaluating GOROOT: ", err)
+	}
 	var files []string
-	err := filepath.Walk(runtime.GOROOT(), func(path string, info os.FileInfo, err error) error {
+	err = filepath.Walk(goroot, func(path string, info os.FileInfo, err error) error {
 		if err != nil {
 			return err
 		}
@@ -53,7 +56,7 @@ func checkZeroMTime(t *testing.T, path string) {
 		return
 	}
 	defer gz.Close()
-	if !gz.ModTime.Equal(time.Unix(0, 0)) {
+	if !gz.ModTime.IsZero() {
 		t.Errorf("gzip file %s has non-zero mtime (%s)", path, gz.ModTime)
 	}
 }