diff --git a/src/compress/gzip/gunzip.go b/src/compress/gzip/gunzip.go
index 4a4f19443d..8ab2b5e5ec 100644
--- a/src/compress/gzip/gunzip.go
+++ b/src/compress/gzip/gunzip.go
@@ -262,16 +262,13 @@ func (z *Reader) Read(p []byte) (n int, err error) {
 	if z.err != nil {
 		return 0, z.err
 	}
-	if len(p) == 0 {
-		return 0, nil
-	}
 
-	n, err = z.decompressor.Read(p)
+	n, z.err = z.decompressor.Read(p)
 	z.digest.Write(p[0:n])
 	z.size += uint32(n)
-	if n != 0 || err != io.EOF {
-		z.err = err
-		return
+	if z.err != io.EOF {
+		// In the normal case we return here.
+		return n, z.err
 	}
 
 	// Finished file; check checksum + size.
@@ -280,28 +277,31 @@ func (z *Reader) Read(p []byte) (n int, err error) {
 			err = io.ErrUnexpectedEOF
 		}
 		z.err = err
-		return 0, err
+		return n, err
 	}
 	crc32, isize := get4(z.buf[0:4]), get4(z.buf[4:8])
 	sum := z.digest.Sum32()
 	if sum != crc32 || isize != z.size {
 		z.err = ErrChecksum
-		return 0, z.err
+		return n, z.err
 	}
-
-	// File is ok; is there another?
-	if !z.multistream {
-		return 0, io.EOF
-	}
-
-	if err = z.readHeader(false); err != nil {
-		z.err = err
-		return
-	}
-
-	// Yes. Reset and read from it.
 	z.digest.Reset()
 	z.size = 0
+
+	// File is ok; check if there is another.
+	if !z.multistream {
+		return n, io.EOF
+	}
+	z.err = nil // Remove io.EOF
+
+	if z.err = z.readHeader(false); z.err != nil {
+		return n, z.err
+	}
+
+	// Read from next file, if necessary.
+	if n > 0 {
+		return n, nil
+	}
 	return z.Read(p)
 }