diff --git a/archive/tar/common.go b/archive/tar/common.go
index e363aa7..c31df06 100644
--- a/archive/tar/common.go
+++ b/archive/tar/common.go
@@ -139,8 +139,8 @@ func (fi headerFileInfo) Mode() (mode os.FileMode) {
 	}
 
 	switch fi.h.Typeflag {
-	case TypeLink, TypeSymlink:
-		// hard link, symbolic link
+	case TypeSymlink:
+		// symbolic link
 		mode |= os.ModeSymlink
 	case TypeChar:
 		// character device node
@@ -249,6 +249,30 @@ func FileInfoHeader(fi os.FileInfo, link string) (*Header, error) {
 	if fm&os.ModeSticky != 0 {
 		h.Mode |= c_ISVTX
 	}
+	// If possible, populate additional fields from OS-specific
+	// FileInfo fields.
+	if sys, ok := fi.Sys().(*Header); ok {
+		// This FileInfo came from a Header (not the OS). Use the
+		// original Header to populate all remaining fields.
+		h.Uid = sys.Uid
+		h.Gid = sys.Gid
+		h.Uname = sys.Uname
+		h.Gname = sys.Gname
+		h.AccessTime = sys.AccessTime
+		h.ChangeTime = sys.ChangeTime
+		if sys.Xattrs != nil {
+			h.Xattrs = make(map[string]string)
+			for k, v := range sys.Xattrs {
+				h.Xattrs[k] = v
+			}
+		}
+		if sys.Typeflag == TypeLink {
+			// hard link
+			h.Typeflag = TypeLink
+			h.Size = 0
+			h.Linkname = sys.Linkname
+		}
+	}
 	if sysStat != nil {
 		return h, sysStat(fi, h)
 	}
diff --git a/archive/tar/reader.go b/archive/tar/reader.go
index c72e002..4168ea2 100644
--- a/archive/tar/reader.go
+++ b/archive/tar/reader.go
@@ -138,7 +138,13 @@ func (tr *Reader) Next() (*Header, error) {
 		// We actually read the whole file,
 		// but this skips alignment padding
 		tr.skipUnread()
+		if tr.err != nil {
+			return nil, tr.err
+		}
 		hdr = tr.readHeader()
+		if hdr == nil {
+			return nil, tr.err
+		}
 		mergePAX(hdr, headers)
 
 		// Check for a PAX format sparse file
@@ -397,7 +403,7 @@ func parsePAX(r io.Reader) (map[string]string, error) {
 		}
 		// Parse the first token as a decimal integer.
 		n, err := strconv.ParseInt(string(buf[:sp]), 10, 0)
-		if err != nil {
+		if err != nil || n < 5 || int64(len(buf)) < n {
 			return nil, ErrHeader
 		}
 		// Extract everything between the decimal and the n -1 on the
@@ -553,6 +559,10 @@ func (tr *Reader) readHeader() *Header {
 	hdr.Uid = int(tr.octal(s.next(8)))
 	hdr.Gid = int(tr.octal(s.next(8)))
 	hdr.Size = tr.octal(s.next(12))
+	if hdr.Size < 0 {
+		tr.err = ErrHeader
+		return nil
+	}
 	hdr.ModTime = time.Unix(tr.octal(s.next(12)), 0)
 	s.next(8) // chksum
 	hdr.Typeflag = s.next(1)[0]
@@ -895,6 +905,9 @@ func (sfr *sparseFileReader) Read(b []byte) (n int, err error) {
 		// Otherwise, we're at the end of the file
 		return 0, io.EOF
 	}
+	if sfr.tot < sfr.sp[0].offset {
+		return 0, io.ErrUnexpectedEOF
+	}
 	if sfr.pos < sfr.sp[0].offset {
 		// We're in a hole
 		n = sfr.readHole(b, sfr.sp[0].offset)
diff --git a/archive/tar/reader_test.go b/archive/tar/reader_test.go
index 9601ffe..da01f26 100644
--- a/archive/tar/reader_test.go
+++ b/archive/tar/reader_test.go
@@ -462,9 +462,14 @@ func TestParsePAXHeader(t *testing.T) {
 			t.Error("Buffer wasn't consumed")
 		}
 	}
-	badHeader := bytes.NewReader([]byte("3 somelongkey="))
-	if _, err := parsePAX(badHeader); err != ErrHeader {
-		t.Fatal("Unexpected success when parsing bad header")
+	badHeaderTests := [][]byte{
+		[]byte("3 somelongkey=\n"),
+		[]byte("50 tooshort=\n"),
+	}
+	for _, test := range badHeaderTests {
+		if _, err := parsePAX(bytes.NewReader(test)); err != ErrHeader {
+			t.Fatal("Unexpected success when parsing bad header")
+		}
 	}
 }
 
@@ -741,3 +746,53 @@ func TestUninitializedRead(t *testing.T) {
 	}
 
 }
+
+// Negative header size should not cause panic.
+// Issues 10959 and 10960.
+func TestNegativeHdrSize(t *testing.T) {
+	f, err := os.Open("testdata/neg-size.tar")
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer f.Close()
+	r := NewReader(f)
+	_, err = r.Next()
+	if err != ErrHeader {
+		t.Error("want ErrHeader, got", err)
+	}
+	io.Copy(ioutil.Discard, r)
+}
+
+// This used to hang in (*sparseFileReader).readHole due to missing
+// verification of sparse offsets against file size.
+func TestIssue10968(t *testing.T) {
+	f, err := os.Open("testdata/issue10968.tar")
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer f.Close()
+	r := NewReader(f)
+	_, err = r.Next()
+	if err != nil {
+		t.Fatal(err)
+	}
+	_, err = io.Copy(ioutil.Discard, r)
+	if err != io.ErrUnexpectedEOF {
+		t.Fatalf("expected %q, got %q", io.ErrUnexpectedEOF, err)
+	}
+}
+
+// Do not panic if there are errors in header blocks after the pax header.
+// Issue 11169
+func TestIssue11169(t *testing.T) {
+	f, err := os.Open("testdata/issue11169.tar")
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer f.Close()
+	r := NewReader(f)
+	_, err = r.Next()
+	if err == nil {
+		t.Fatal("Unexpected success")
+	}
+}
diff --git a/archive/tar/tar_test.go b/archive/tar/tar_test.go
index ed333f3..d63c072 100644
--- a/archive/tar/tar_test.go
+++ b/archive/tar/tar_test.go
@@ -147,17 +147,6 @@ func TestHeaderRoundTrip(t *testing.T) {
 			},
 			fm: 0644,
 		},
-		// hard link.
-		{
-			h: &Header{
-				Name:     "hard.txt",
-				Mode:     0644 | c_ISLNK,
-				Size:     0,
-				ModTime:  time.Unix(1360600916, 0),
-				Typeflag: TypeLink,
-			},
-			fm: 0644 | os.ModeSymlink,
-		},
 		// symbolic link.
 		{
 			h: &Header{
@@ -246,6 +235,33 @@ func TestHeaderRoundTrip(t *testing.T) {
 			},
 			fm: 0600 | os.ModeSticky,
 		},
+		// hard link.
+		{
+			h: &Header{
+				Name:     "hard.txt",
+				Mode:     0644 | c_ISREG,
+				Size:     0,
+				Linkname: "file.txt",
+				ModTime:  time.Unix(1360600916, 0),
+				Typeflag: TypeLink,
+			},
+			fm: 0644,
+		},
+		// More information.
+		{
+			h: &Header{
+				Name:     "info.txt",
+				Mode:     0600 | c_ISREG,
+				Size:     0,
+				Uid:      1000,
+				Gid:      1000,
+				ModTime:  time.Unix(1360602540, 0),
+				Uname:    "slartibartfast",
+				Gname:    "users",
+				Typeflag: TypeReg,
+			},
+			fm: 0600,
+		},
 	}
 
 	for i, g := range golden {
@@ -268,12 +284,37 @@ func TestHeaderRoundTrip(t *testing.T) {
 		if got, want := h2.Size, g.h.Size; got != want {
 			t.Errorf("i=%d: Size: got %v, want %v", i, got, want)
 		}
+		if got, want := h2.Uid, g.h.Uid; got != want {
+			t.Errorf("i=%d: Uid: got %d, want %d", i, got, want)
+		}
+		if got, want := h2.Gid, g.h.Gid; got != want {
+			t.Errorf("i=%d: Gid: got %d, want %d", i, got, want)
+		}
+		if got, want := h2.Uname, g.h.Uname; got != want {
+			t.Errorf("i=%d: Uname: got %q, want %q", i, got, want)
+		}
+		if got, want := h2.Gname, g.h.Gname; got != want {
+			t.Errorf("i=%d: Gname: got %q, want %q", i, got, want)
+		}
+		if got, want := h2.Linkname, g.h.Linkname; got != want {
+			t.Errorf("i=%d: Linkname: got %v, want %v", i, got, want)
+		}
+		if got, want := h2.Typeflag, g.h.Typeflag; got != want {
+			t.Logf("%#v %#v", g.h, fi.Sys())
+			t.Errorf("i=%d: Typeflag: got %q, want %q", i, got, want)
+		}
 		if got, want := h2.Mode, g.h.Mode; got != want {
 			t.Errorf("i=%d: Mode: got %o, want %o", i, got, want)
 		}
 		if got, want := fi.Mode(), g.fm; got != want {
 			t.Errorf("i=%d: fi.Mode: got %o, want %o", i, got, want)
 		}
+		if got, want := h2.AccessTime, g.h.AccessTime; got != want {
+			t.Errorf("i=%d: AccessTime: got %v, want %v", i, got, want)
+		}
+		if got, want := h2.ChangeTime, g.h.ChangeTime; got != want {
+			t.Errorf("i=%d: ChangeTime: got %v, want %v", i, got, want)
+		}
 		if got, want := h2.ModTime, g.h.ModTime; got != want {
 			t.Errorf("i=%d: ModTime: got %v, want %v", i, got, want)
 		}
diff --git a/archive/tar/testdata/hardlink.tar b/archive/tar/testdata/hardlink.tar
new file mode 100644
index 0000000..9cd1a26
Binary files /dev/null and b/archive/tar/testdata/hardlink.tar differ
diff --git a/archive/tar/testdata/issue10968.tar b/archive/tar/testdata/issue10968.tar
new file mode 100644
index 0000000..1cc837b
Binary files /dev/null and b/archive/tar/testdata/issue10968.tar differ
diff --git a/archive/tar/testdata/issue11169.tar b/archive/tar/testdata/issue11169.tar
new file mode 100644
index 0000000..4d71fa1
Binary files /dev/null and b/archive/tar/testdata/issue11169.tar differ
diff --git a/archive/tar/testdata/neg-size.tar b/archive/tar/testdata/neg-size.tar
new file mode 100644
index 0000000..5deea3d
Binary files /dev/null and b/archive/tar/testdata/neg-size.tar differ
diff --git a/archive/tar/writer.go b/archive/tar/writer.go
index dafb2ca..9dbc01a 100644
--- a/archive/tar/writer.go
+++ b/archive/tar/writer.go
@@ -355,7 +355,7 @@ func paxHeader(msg string) string {
 // hdr.Size bytes are written after WriteHeader.
 func (tw *Writer) Write(b []byte) (n int, err error) {
 	if tw.closed {
-		err = ErrWriteTooLong
+		err = ErrWriteAfterClose
 		return
 	}
 	overwrite := false
diff --git a/archive/tar/writer_test.go b/archive/tar/writer_test.go
index 5e42e32..fe46a67 100644
--- a/archive/tar/writer_test.go
+++ b/archive/tar/writer_test.go
@@ -147,6 +147,44 @@ var writerTests = []*writerTest{
 			},
 		},
 	},
+	// This file was produced using gnu tar 1.26
+	// echo "Slartibartfast" > file.txt
+	// ln file.txt hard.txt
+	// tar -b 1 --format=ustar -c -f hardlink.tar file.txt hard.txt
+	{
+		file: "testdata/hardlink.tar",
+		entries: []*writerTestEntry{
+			{
+				header: &Header{
+					Name:     "file.txt",
+					Mode:     0644,
+					Uid:      1000,
+					Gid:      100,
+					Size:     15,
+					ModTime:  time.Unix(1425484303, 0),
+					Typeflag: '0',
+					Uname:    "vbatts",
+					Gname:    "users",
+				},
+				contents: "Slartibartfast\n",
+			},
+			{
+				header: &Header{
+					Name:     "hard.txt",
+					Mode:     0644,
+					Uid:      1000,
+					Gid:      100,
+					Size:     0,
+					ModTime:  time.Unix(1425484303, 0),
+					Typeflag: '1',
+					Linkname: "file.txt",
+					Uname:    "vbatts",
+					Gname:    "users",
+				},
+				// no contents
+			},
+		},
+	},
 }
 
 // Render byte array in a two-character hexadecimal string, spaced for easy visual inspection.
@@ -489,3 +527,20 @@ func TestValidTypeflagWithPAXHeader(t *testing.T) {
 		}
 	}
 }
+
+func TestWriteAfterClose(t *testing.T) {
+	var buffer bytes.Buffer
+	tw := NewWriter(&buffer)
+
+	hdr := &Header{
+		Name: "small.txt",
+		Size: 5,
+	}
+	if err := tw.WriteHeader(hdr); err != nil {
+		t.Fatalf("Failed to write header: %s", err)
+	}
+	tw.Close()
+	if _, err := tw.Write([]byte("Kilts")); err != ErrWriteAfterClose {
+		t.Fatalf("Write: got %v; want ErrWriteAfterClose", err)
+	}
+}