diff --git a/src/Makefile b/src/Makefile
index 28075d36..65ab754f 100644
--- a/src/Makefile
+++ b/src/Makefile
@@ -142,6 +142,7 @@ XCFLAGS=
 #
 # This define is required to run LuaJIT under Valgrind. The Valgrind
 # header files must be installed. You should enable debug information, too.
+# Use --suppressions=lj.supp to avoid some false positives.
 #XCFLAGS+= -DLUAJIT_USE_VALGRIND
 #
 # This is the client for the GDB JIT API. GDB 7.0 or higher is required
diff --git a/src/lj.supp b/src/lj.supp
index f1126ad7..411f2617 100644
--- a/src/lj.supp
+++ b/src/lj.supp
@@ -1,14 +1,24 @@
-# Valgrind suppression file for LuaJIT 2.x.
+# Valgrind suppression file for LuaJIT 2.0.
 {
    Optimized string compare
    Memcheck:Addr4
    fun:lj_str_cmp
 }
+{
+   Optimized string compare
+   Memcheck:Addr1
+   fun:lj_str_cmp
+}
 {
    Optimized string compare
    Memcheck:Addr4
    fun:lj_str_new
 }
+{
+   Optimized string compare
+   Memcheck:Addr1
+   fun:lj_str_new
+}
 {
    Optimized string compare
    Memcheck:Cond