diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h
index 608d19b..7f3d5cd 100644
--- a/src/ecmult_impl.h
+++ b/src/ecmult_impl.h
@@ -567,7 +567,9 @@ static size_t secp256k1_strauss_max_points(secp256k1_scratch *scratch) {
  */
 static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) {
     int skew = 0;
-    int pos = 1;
+    int pos;
+    int max_pos;
+    int last_w;
     const secp256k1_scalar *work = s;
 
     if (secp256k1_scalar_is_zero(s)) {
@@ -582,14 +584,24 @@ static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) {
     }
 
     wnaf[0] = secp256k1_scalar_get_bits_var(work, 0, w) + skew;
+    /* Compute last window size. Relevant when window size doesn't divide the
+     * number of bits in the scalar */
+    last_w = WNAF_BITS - (WNAF_SIZE(w) - 1) * w;
 
-    while (pos * w < WNAF_BITS) {
-        int now = w;
-        int val;
-        if (now + pos * w > WNAF_BITS) {
-            now = WNAF_BITS - pos * w;
+    /* Store the position of the first nonzero word in max_pos to allow
+     * skipping leading zeros when calculating the wnaf. */
+    for (pos = WNAF_SIZE(w) - 1; pos > 0; pos--) {
+        int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
+        if(val != 0) {
+            break;
         }
-        val = secp256k1_scalar_get_bits_var(work, pos * w, now);
+        wnaf[pos] = 0;
+    }
+    max_pos = pos;
+    pos = 1;
+
+    while (pos <= max_pos) {
+        int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
         if ((val & 1) == 0) {
             wnaf[pos - 1] -= (1 << w);
             wnaf[pos] = (val + 1);
@@ -611,7 +623,6 @@ static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) {
         }
         ++pos;
     }
-    VERIFY_CHECK(pos == WNAF_SIZE(w));
 
     return skew;
 }
diff --git a/src/tests.c b/src/tests.c
index ed88811..13d1a91 100644
--- a/src/tests.c
+++ b/src/tests.c
@@ -3040,7 +3040,20 @@ void test_fixed_wnaf(const secp256k1_scalar *number, int w) {
     CHECK(secp256k1_scalar_eq(&x, &num));
 }
 
-void test_fixed_wnaf_zero(int w) {
+/* Checks that the first 8 elements of wnaf are equal to wnaf_expected and the
+ * rest is 0.*/
+void test_fixed_wnaf_small_helper(int *wnaf, int *wnaf_expected, int w) {
+    int i;
+    for (i = WNAF_SIZE(w)-1; i >= 8; --i) {
+        CHECK(wnaf[i] == 0);
+    }
+    for (i = 7; i >= 0; --i) {
+        CHECK(wnaf[i] == wnaf_expected[i]);
+    }
+}
+
+void test_fixed_wnaf_small(void) {
+    int w = 4;
     int wnaf[256] = {0};
     int i;
     int skew;
@@ -3048,12 +3061,49 @@ void test_fixed_wnaf_zero(int w) {
 
     secp256k1_scalar_set_int(&num, 0);
     skew = secp256k1_wnaf_fixed(wnaf, &num, w);
-
     for (i = WNAF_SIZE(w)-1; i >= 0; --i) {
         int v = wnaf[i];
         CHECK(v == 0);
     }
     CHECK(skew == 0);
+
+    secp256k1_scalar_set_int(&num, 1);
+    skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+    for (i = WNAF_SIZE(w)-1; i >= 1; --i) {
+        int v = wnaf[i];
+        CHECK(v == 0);
+    }
+    CHECK(wnaf[0] == 1);
+    CHECK(skew == 0);
+
+    {
+        int wnaf_expected[8] = { 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf, 0xf };
+        secp256k1_scalar_set_int(&num, 0xffffffff);
+        skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+        test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
+        CHECK(skew == 0);
+    }
+    {
+        int wnaf_expected[8] = { -1, -1, -1, -1, -1, -1, -1, 0xf };
+        secp256k1_scalar_set_int(&num, 0xeeeeeeee);
+        skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+        test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
+        CHECK(skew == 1);
+    }
+    {
+        int wnaf_expected[8] = { 1, 0, 1, 0, 1, 0, 1, 0 };
+        secp256k1_scalar_set_int(&num, 0x01010101);
+        skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+        test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
+        CHECK(skew == 0);
+    }
+    {
+        int wnaf_expected[8] = { -0xf, 0, 0xf, -0xf, 0, 0xf, 1, 0 };
+        secp256k1_scalar_set_int(&num, 0x01ef1ef1);
+        skew = secp256k1_wnaf_fixed(wnaf, &num, w);
+        test_fixed_wnaf_small_helper(wnaf, wnaf_expected, w);
+        CHECK(skew == 0);
+    }
 }
 
 void run_wnaf(void) {
@@ -3067,7 +3117,7 @@ void run_wnaf(void) {
     n.d[0] = 2;
     test_constant_wnaf(&n, 4);
     /* Test 0 */
-    test_fixed_wnaf_zero(4);
+    test_fixed_wnaf_small();
     /* Random tests */
     for (i = 0; i < count; i++) {
         random_scalar_order(&n);