diff --git a/src/debug/elf/elf_test.go b/src/debug/elf/elf_test.go
index b8c310dba5..a61b491090 100644
--- a/src/debug/elf/elf_test.go
+++ b/src/debug/elf/elf_test.go
@@ -47,25 +47,3 @@ func TestNames(t *testing.T) {
 		}
 	}
 }
-
-func TestNobitsSection(t *testing.T) {
-	const testdata = "testdata/gcc-amd64-linux-exec"
-	f, err := Open(testdata)
-	if err != nil {
-		t.Fatalf("could not read %s: %v", testdata, err)
-	}
-	defer f.Close()
-	bss := f.Section(".bss")
-	bssData, err := bss.Data()
-	if err != nil {
-		t.Fatalf("error reading .bss section: %v", err)
-	}
-	if g, w := uint64(len(bssData)), bss.Size; g != w {
-		t.Errorf(".bss section length mismatch: got %d, want %d", g, w)
-	}
-	for i := range bssData {
-		if bssData[i] != 0 {
-			t.Fatalf("unexpected non-zero byte at offset %d: %#x", i, bssData[i])
-		}
-	}
-}
diff --git a/src/debug/elf/file.go b/src/debug/elf/file.go
index db07a2daff..83a3cbc0b8 100644
--- a/src/debug/elf/file.go
+++ b/src/debug/elf/file.go
@@ -102,6 +102,8 @@ type Section struct {
 // Data reads and returns the contents of the ELF section.
 // Even if the section is stored compressed in the ELF file,
 // Data returns uncompressed data.
+//
+// For an SHT_NOBITS section, Data always returns a non-nil error.
 func (s *Section) Data() ([]byte, error) {
 	return saferio.ReadData(s.Open(), s.Size)
 }
@@ -118,9 +120,12 @@ func (f *File) stringTable(link uint32) ([]byte, error) {
 // Open returns a new ReadSeeker reading the ELF section.
 // Even if the section is stored compressed in the ELF file,
 // the ReadSeeker reads uncompressed data.
+//
+// For an SHT_NOBITS section, all calls to the opened reader
+// will return a non-nil error.
 func (s *Section) Open() io.ReadSeeker {
 	if s.Type == SHT_NOBITS {
-		return io.NewSectionReader(&zeroReader{}, 0, int64(s.Size))
+		return io.NewSectionReader(&nobitsSectionReader{}, 0, int64(s.Size))
 	}
 	if s.Flags&SHF_COMPRESSED == 0 {
 		return io.NewSectionReader(s.sr, 0, 1<<63-1)
@@ -1602,11 +1607,8 @@ func (f *File) DynString(tag DynTag) ([]string, error) {
 	return all, nil
 }
 
-type zeroReader struct{}
+type nobitsSectionReader struct{}
 
-func (*zeroReader) ReadAt(p []byte, off int64) (n int, err error) {
-	for i := range p {
-		p[i] = 0
-	}
-	return len(p), nil
+func (*nobitsSectionReader) ReadAt(p []byte, off int64) (n int, err error) {
+	return 0, errors.New("unexpected read from SHT_NOBITS section")
 }
diff --git a/src/debug/elf/file_test.go b/src/debug/elf/file_test.go
index fe72a1908f..282e1fccd9 100644
--- a/src/debug/elf/file_test.go
+++ b/src/debug/elf/file_test.go
@@ -945,6 +945,30 @@ func TestNoSectionOverlaps(t *testing.T) {
 	}
 }
 
+func TestNobitsSection(t *testing.T) {
+	const testdata = "testdata/gcc-amd64-linux-exec"
+	f, err := Open(testdata)
+	if err != nil {
+		t.Fatalf("could not read %s: %v", testdata, err)
+	}
+	defer f.Close()
+
+	wantError := "unexpected read from SHT_NOBITS section"
+	bss := f.Section(".bss")
+
+	_, err = bss.Data()
+	if err == nil || err.Error() != wantError {
+		t.Fatalf("bss.Data() got error %q, want error %q", err, wantError)
+	}
+
+	r := bss.Open()
+	p := make([]byte, 1)
+	_, err = r.Read(p)
+	if err == nil || err.Error() != wantError {
+		t.Fatalf("r.Read(p) got error %q, want error %q", err, wantError)
+	}
+}
+
 // TestLargeNumberOfSections tests the case that a file has greater than or
 // equal to 65280 (0xff00) sections.
 func TestLargeNumberOfSections(t *testing.T) {