diff --git a/src/field.h b/src/field.h
index 854aaebabc966..55679a2fc130a 100644
--- a/src/field.h
+++ b/src/field.h
@@ -14,8 +14,8 @@
  *  - Each field element can be normalized or not.
  *  - Each field element has a magnitude, which represents how far away
  *    its representation is away from normalization. Normalized elements
- *    always have a magnitude of 1, but a magnitude of 1 doesn't imply
- *    normality.
+ *    always have a magnitude of 0 or 1, but a magnitude of 1 doesn't
+ *    imply normality.
  */
 
 #if defined HAVE_CONFIG_H
@@ -50,7 +50,9 @@ static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r);
  *  without constant-time guarantee. */
 static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r);
 
-/** Set a field element equal to a small integer. Resulting field element is normalized. */
+/** Set a field element equal to a small (not greater than 0x7FFF), non-negative integer.
+ *  Resulting field element is normalized; it has magnitude 0 if a == 0, and magnitude 1 otherwise.
+ */
 static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
 
 /** Sets a field element equal to zero, initializing all fields. */
diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h
index 724474906145e..4363e727e76e8 100644
--- a/src/field_10x26_impl.h
+++ b/src/field_10x26_impl.h
@@ -264,10 +264,11 @@ static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
 }
 
 SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
+    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = r->n[5] = r->n[6] = r->n[7] = r->n[8] = r->n[9] = 0;
 #ifdef VERIFY
-    r->magnitude = 1;
+    r->magnitude = (a != 0);
     r->normalized = 1;
     secp256k1_fe_verify(r);
 #endif
diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h
index ed52297e959e2..b56bdd13534c4 100644
--- a/src/field_5x52_impl.h
+++ b/src/field_5x52_impl.h
@@ -227,10 +227,11 @@ static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
 }
 
 SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
+    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
     r->n[0] = a;
     r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
 #ifdef VERIFY
-    r->magnitude = 1;
+    r->magnitude = (a != 0);
     r->normalized = 1;
     secp256k1_fe_verify(r);
 #endif