diff --git a/src/hb-map.hh b/src/hb-map.hh
index 9ffa83a8a..bbb1bef5d 100644
--- a/src/hb-map.hh
+++ b/src/hb-map.hh
@@ -34,11 +34,9 @@
  * hb_hashmap_t
  */
 
-/* TODO if K/V is signed integer, -1 is not a good default.
- * Don't know how to get to -MAX using bit work. */
 template <typename K, typename V,
-	  K kINVALID = hb_is_pointer (K) ? 0 : (K) -1,
-	  V vINVALID = hb_is_pointer (V) ? 0 : (V) -1>
+	  K kINVALID = hb_is_pointer (K) ? 0 : hb_is_signed (K) ? hb_int_min (K) : (K) -1,
+	  V vINVALID = hb_is_pointer (V) ? 0 : hb_is_signed (V) ? hb_int_min (V) : (V) -1>
 struct hb_hashmap_t
 {
   HB_DELETE_COPY_ASSIGN (hb_hashmap_t);
diff --git a/src/hb-meta.hh b/src/hb-meta.hh
index 0dcf79320..bb67b03a8 100644
--- a/src/hb-meta.hh
+++ b/src/hb-meta.hh
@@ -138,6 +138,12 @@ template <> struct hb_is_signed<uint32_t> { enum { value = false }; };
 template <> struct hb_is_signed<uint64_t> { enum { value = false }; };
 #define hb_is_signed(T) hb_is_signed<T>::value
 
+template <typename T> struct hb_int_min { static constexpr T value = 0; };
+template <> struct hb_int_min<char> { static constexpr char value = CHAR_MIN; };
+template <> struct hb_int_min<int>  { static constexpr int  value = INT_MIN;  };
+template <> struct hb_int_min<long> { static constexpr long value = LONG_MIN; };
+#define hb_int_min(T) hb_int_min<T>::value
+
 template <bool is_signed> struct hb_signedness_int;
 template <> struct hb_signedness_int<false> { typedef unsigned int value; };
 template <> struct hb_signedness_int<true>  { typedef   signed int value; };
diff --git a/src/hb-ot-cff1-table.cc b/src/hb-ot-cff1-table.cc
index 5132801bf..1d97e5444 100644
--- a/src/hb-ot-cff1-table.cc
+++ b/src/hb-ot-cff1-table.cc
@@ -26,7 +26,6 @@
 
 #include "hb-ot-cff1-table.hh"
 #include "hb-cff1-interp-cs.hh"
-#include <limits.h>
 
 using namespace CFF;
 
diff --git a/src/hb-ot-cff2-table.cc b/src/hb-ot-cff2-table.cc
index 15cdbaa85..d2463d785 100644
--- a/src/hb-ot-cff2-table.cc
+++ b/src/hb-ot-cff2-table.cc
@@ -26,7 +26,6 @@
 
 #include "hb-ot-cff2-table.hh"
 #include "hb-cff2-interp-cs.hh"
-#include <limits.h>
 
 using namespace CFF;
 
diff --git a/src/hb.hh b/src/hb.hh
index ee35c4dd9..0336ed568 100644
--- a/src/hb.hh
+++ b/src/hb.hh
@@ -167,8 +167,7 @@
 #include "hb-aat.h"
 #define HB_AAT_H_IN
 
-#include "hb-aat.h"
-
+#include <limits.h>
 #include <math.h>
 #include <stdlib.h>
 #include <stddef.h>