diff --git a/src/tests.c b/src/tests.c
index 2f2cb71539049..1040b6e508df8 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -3190,6 +3190,7 @@ void test_constant_wnaf(const secp256k1_scalar *number, int w) {
     int skew;
     int bits = 256;
     secp256k1_scalar num = *number;
+    secp256k1_scalar scalar_skew;
 
     secp256k1_scalar_set_int(&x, 0);
     secp256k1_scalar_set_int(&shift, 1 << w);
@@ -3220,7 +3221,8 @@ void test_constant_wnaf(const secp256k1_scalar *number, int w) {
         secp256k1_scalar_add(&x, &x, &t);
     }
     /* Skew num because when encoding numbers as odd we use an offset */
-    secp256k1_scalar_cadd_bit(&num, skew == 2, 1);
+    secp256k1_scalar_set_int(&scalar_skew, 1 << (skew == 2));
+    secp256k1_scalar_add(&num, &num, &scalar_skew);
     CHECK(secp256k1_scalar_eq(&x, &num));
 }
 
@@ -3332,13 +3334,32 @@ void run_wnaf(void) {
     int i;
     secp256k1_scalar n = {{0}};
 
+    test_constant_wnaf(&n, 4);
     /* Sanity check: 1 and 2 are the smallest odd and even numbers and should
      *               have easier-to-diagnose failure modes  */
     n.d[0] = 1;
     test_constant_wnaf(&n, 4);
     n.d[0] = 2;
     test_constant_wnaf(&n, 4);
-    /* Test 0 */
+    /* Test -1, because it's a special case in wnaf_const */
+    n = secp256k1_scalar_one;
+    secp256k1_scalar_negate(&n, &n);
+    test_constant_wnaf(&n, 4);
+
+    /* Test -2, which may not lead to overflows in wnaf_const */
+    secp256k1_scalar_add(&n, &secp256k1_scalar_one, &secp256k1_scalar_one);
+    secp256k1_scalar_negate(&n, &n);
+    test_constant_wnaf(&n, 4);
+
+    /* Test (1/2) - 1 = 1/-2 and 1/2 = (1/-2) + 1
+       as corner cases of negation handling in wnaf_const */
+    secp256k1_scalar_inverse(&n, &n);
+    test_constant_wnaf(&n, 4);
+
+    secp256k1_scalar_add(&n, &n, &secp256k1_scalar_one);
+    test_constant_wnaf(&n, 4);
+
+    /* Test 0 for fixed wnaf */
     test_fixed_wnaf_small();
     /* Random tests */
     for (i = 0; i < count; i++) {