diff --git a/src/compress/lzw/reader.go b/src/compress/lzw/reader.go
index 9eef2b2a782..557955bc3fd 100644
--- a/src/compress/lzw/reader.go
+++ b/src/compress/lzw/reader.go
@@ -57,8 +57,14 @@ type decoder struct {
 	// The next two codes mean clear and EOF.
 	// Other valid codes are in the range [lo, hi] where lo := clear + 2,
 	// with the upper bound incrementing on each code seen.
-	// overflow is the code at which hi overflows the code width.
+	//
+	// overflow is the code at which hi overflows the code width. It always
+	// equals 1 << width.
+	//
 	// last is the most recently seen code, or decoderInvalidCode.
+	//
+	// An invariant is that
+	// (hi < overflow) || (hi == overflow && last == decoderInvalidCode)
 	clear, eof, hi, overflow, last uint16
 
 	// Each code c in [lo, hi] expands to two or more bytes. For c != hi:
@@ -196,6 +202,10 @@ loop:
 		if d.hi >= d.overflow {
 			if d.width == maxWidth {
 				d.last = decoderInvalidCode
+				// Undo the d.hi++ a few lines above, so that (1) we maintain
+				// the invariant that d.hi <= d.overflow, and (2) d.hi does not
+				// eventually overflow a uint16.
+				d.hi--
 			} else {
 				d.width++
 				d.overflow <<= 1
diff --git a/src/compress/lzw/reader_test.go b/src/compress/lzw/reader_test.go
index 6b9f9a3da70..53c9cdd865d 100644
--- a/src/compress/lzw/reader_test.go
+++ b/src/compress/lzw/reader_test.go
@@ -120,6 +120,32 @@ func TestReader(t *testing.T) {
 	}
 }
 
+type devZero struct{}
+
+func (devZero) Read(p []byte) (int, error) {
+	for i := range p {
+		p[i] = 0
+	}
+	return len(p), nil
+}
+
+func TestHiCodeDoesNotOverflow(t *testing.T) {
+	r := NewReader(devZero{}, LSB, 8)
+	d := r.(*decoder)
+	buf := make([]byte, 1024)
+	oldHi := uint16(0)
+	for i := 0; i < 100; i++ {
+		if _, err := io.ReadFull(r, buf); err != nil {
+			t.Fatalf("i=%d: %v", i, err)
+		}
+		// The hi code should never decrease.
+		if d.hi < oldHi {
+			t.Fatalf("i=%d: hi=%d decreased from previous value %d", i, d.hi, oldHi)
+		}
+		oldHi = d.hi
+	}
+}
+
 func BenchmarkDecoder(b *testing.B) {
 	buf, err := ioutil.ReadFile("../testdata/e.txt")
 	if err != nil {