diff --git a/tests/leb128.c b/tests/leb128.c
index 6994a436..47b57c0d 100644
--- a/tests/leb128.c
+++ b/tests/leb128.c
@@ -18,6 +18,7 @@
 #include <config.h>
 #include <stddef.h>
 #include <stdbool.h>
+#include <stdint.h>
 #include <libdw.h>
 #include "../libdw/libdwP.h"
 #include "../libdw/memory-access.h"
@@ -26,10 +27,16 @@
 #define FAIL 1
 
 static const unsigned char v0[] = { 0x0 };
+static const unsigned char v1[] = { 0x1 };
 static const unsigned char v23[] = { 23 };
+static const unsigned char vm_1[] = { 0x7f };
 static const unsigned char vm_2[] = { 0x7e };
+static const unsigned char s127[] = { 0xff, 0x00 };
 static const unsigned char v128[] = { 0x80, 0x01 };
+static const unsigned char v129[] = { 0x81, 0x01 };
+static const unsigned char vm_127[] = { 0x81, 0x7f };
 static const unsigned char vm_128[] = { 0x80, 0x7f };
+static const unsigned char vm_129[] = { 0xff, 0x7e };
 static const unsigned char vhuge[] =
   {
     0xff, 0xff, 0xff, 0xff, 0xff,
@@ -50,6 +57,16 @@ static const unsigned char minus_one[] =
     0xff, 0xff, 0xff, 0xff, 0xff,
     0xff, 0xff, 0xff, 0x7f
   };
+static const unsigned char int64_max_m1[] =
+  {
+    0xfe, 0xff, 0xff, 0xff, 0xff,
+    0xff, 0xff, 0xff, 0xff, 0x00
+  };
+static const unsigned char int64_min_p1[] =
+  {
+    0x81, 0x80, 0x80, 0x80, 0x80,
+    0x80, 0x80, 0x80, 0x80, 0x7f
+  };
 
 static int
 test_one_sleb (const unsigned char *data, size_t len, int64_t expect)
@@ -78,14 +95,22 @@ test_sleb (void)
     return FAIL;
 
   TEST (v0, 0);
+  TEST (v1, 1);
   TEST (v23, 23);
+  TEST (vm_1, -1);
   TEST (vm_2, -2);
+  TEST (s127, 127);
   TEST (v128, 128);
+  TEST (v129, 129);
+  TEST (vm_127, -127);
   TEST (vm_128, -128);
+  TEST (vm_129, -129);
   TEST (vhuge, 9223372036854775807ll);
   TEST (most_positive, 4611686018427387903ll);
   TEST (most_negative, -4611686018427387904ll);
   TEST (minus_one, -1);
+  TEST (int64_max_m1, INT64_MAX - 1);
+  TEST (int64_min_p1, INT64_MIN + 1);
 
 #undef TEST
 
@@ -119,14 +144,22 @@ test_uleb (void)
     return FAIL;
 
   TEST (v0, 0);
+  TEST (v1, 1);
   TEST (v23, 23);
+  TEST (vm_1, 127);
   TEST (vm_2, 126);
+  TEST (s127, 127);
   TEST (v128, 128);
+  TEST (v129, 129);
+  TEST (vm_127, 16257);
   TEST (vm_128, 16256);
+  TEST (vm_129, 16255);
   TEST (vhuge, 9223372036854775807ull);
   TEST (most_positive, 4611686018427387903ull);
   TEST (most_negative, 4611686018427387904ull);
   TEST (minus_one, 9223372036854775807ull);
+  TEST (int64_max_m1, INT64_MAX - 1);
+  TEST (int64_min_p1, INT64_MIN + 1);
 
 #undef TEST