diff --git a/src/field.h b/src/field.h
index b1bc4b979e..2c1e9d2e1a 100644
--- a/src/field.h
+++ b/src/field.h
@@ -88,6 +88,7 @@ static const secp256k1_fe secp256k1_const_beta = SECP256K1_FE_CONST(
 #  define secp256k1_fe_set_b32 secp256k1_fe_impl_set_b32
 #  define secp256k1_fe_get_b32 secp256k1_fe_impl_get_b32
 #  define secp256k1_fe_negate secp256k1_fe_impl_negate
+#  define secp256k1_fe_mul_int secp256k1_fe_impl_mul_int
 #endif /* !defined(VERIFY) */
 
 /** Normalize a field element.
@@ -205,8 +206,13 @@ static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
 /** Adds a small integer (up to 0x7FFF) to r. The resulting magnitude increases by one. */
 static void secp256k1_fe_add_int(secp256k1_fe *r, int a);
 
-/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
- *  small integer. */
+/** Multiply a field element with a small integer.
+ *
+ * On input, r must be a valid field element. a must be an integer in [0,32].
+ * The magnitude of r times a must not exceed 32.
+ * Performs {r *= a}.
+ * On output, r's magnitude is multiplied by a, and r will not be normalized.
+ */
 static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);
 
 /** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h
index 9e29f6adf9..f8c8ddb5b4 100644
--- a/src/field_10x26_impl.h
+++ b/src/field_10x26_impl.h
@@ -370,7 +370,7 @@ SECP256K1_INLINE static void secp256k1_fe_impl_negate(secp256k1_fe *r, const sec
     r->n[9] = 0x03FFFFFUL * 2 * (m + 1) - a->n[9];
 }
 
-SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_impl_mul_int(secp256k1_fe *r, int a) {
     r->n[0] *= a;
     r->n[1] *= a;
     r->n[2] *= a;
@@ -381,11 +381,6 @@ SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
     r->n[7] *= a;
     r->n[8] *= a;
     r->n[9] *= a;
-#ifdef VERIFY
-    r->magnitude *= a;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
 SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h
index 4775ee0cee..f509137340 100644
--- a/src/field_5x52_impl.h
+++ b/src/field_5x52_impl.h
@@ -333,17 +333,12 @@ SECP256K1_INLINE static void secp256k1_fe_impl_negate(secp256k1_fe *r, const sec
     r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
 }
 
-SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
+SECP256K1_INLINE static void secp256k1_fe_impl_mul_int(secp256k1_fe *r, int a) {
     r->n[0] *= a;
     r->n[1] *= a;
     r->n[2] *= a;
     r->n[3] *= a;
     r->n[4] *= a;
-#ifdef VERIFY
-    r->magnitude *= a;
-    r->normalized = 0;
-    secp256k1_fe_verify(r);
-#endif
 }
 
 SECP256K1_INLINE static void secp256k1_fe_add_int(secp256k1_fe *r, int a) {
diff --git a/src/field_impl.h b/src/field_impl.h
index 1c70795169..8bd18c61ab 100644
--- a/src/field_impl.h
+++ b/src/field_impl.h
@@ -264,6 +264,17 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k
     r->normalized = 0;
     secp256k1_fe_verify(r);
 }
+
+static void secp256k1_fe_impl_mul_int(secp256k1_fe *r, int a);
+SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) {
+    secp256k1_fe_verify(r);
+    VERIFY_CHECK(a >= 0 && a <= 32);
+    VERIFY_CHECK(a*r->magnitude <= 32);
+    secp256k1_fe_impl_mul_int(r, a);
+    r->magnitude *= a;
+    r->normalized = 0;
+    secp256k1_fe_verify(r);
+}
 #endif /* defined(VERIFY) */
 
 #endif /* SECP256K1_FIELD_IMPL_H */