diff --git a/src/ecmult_const_impl.h b/src/ecmult_const_impl.h
index 011ccf0..6d6d354 100644
--- a/src/ecmult_const_impl.h
+++ b/src/ecmult_const_impl.h
@@ -14,7 +14,7 @@
 
 /* This is like `ECMULT_TABLE_GET_GE` but is constant time */
 #define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \
-    int m; \
+    int m = 0; \
     /* Extract the sign-bit for a constant time absolute-value. */ \
     int mask = (n) >> (sizeof(n) * CHAR_BIT - 1); \
     int abs_n = ((n) + mask) ^ mask; \
@@ -25,7 +25,11 @@
     VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1)); \
     VERIFY_SETUP(secp256k1_fe_clear(&(r)->x)); \
     VERIFY_SETUP(secp256k1_fe_clear(&(r)->y)); \
-    for (m = 0; m < ECMULT_TABLE_SIZE(w); m++) { \
+    /* Unconditionally set r->x = (pre)[m].x. r->y = (pre)[m].y. because it's either the correct one \
+     * or will get replaced in the later iterations, this is needed to make sure `r` is initialized. */ \
+    (r)->x = (pre)[m].x; \
+    (r)->y = (pre)[m].y; \
+    for (m = 1; m < ECMULT_TABLE_SIZE(w); m++) { \
         /* This loop is used to avoid secret data in array indices. See
          * the comment in ecmult_gen_impl.h for rationale. */ \
         secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == idx_n); \
diff --git a/src/field.h b/src/field.h
index 8283e4b..7993a1f 100644
--- a/src/field.h
+++ b/src/field.h
@@ -125,10 +125,10 @@ static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe
 /** Convert a field element back from the storage type. */
 static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
 
-/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized.*/
 static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
 
-/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized.*/
 static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
 
 #endif /* SECP256K1_FIELD_H */
diff --git a/src/group.h b/src/group.h
index ded4e1d..863644f 100644
--- a/src/group.h
+++ b/src/group.h
@@ -132,7 +132,7 @@ static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge
 /** Convert a group element back from the storage type. */
 static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
 
-/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized.*/
 static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
 
 /** Rescale a jacobian point by b which must be non-zero. Constant-time. */
diff --git a/src/scalar.h b/src/scalar.h
index 6dc7574..2a74703 100644
--- a/src/scalar.h
+++ b/src/scalar.h
@@ -111,7 +111,7 @@ static void secp256k1_scalar_split_lambda(secp256k1_scalar *r1, secp256k1_scalar
 /** Multiply a and b (without taking the modulus!), divide by 2**shift, and round to the nearest integer. Shift must be at least 256. */
 static void secp256k1_scalar_mul_shift_var(secp256k1_scalar *r, const secp256k1_scalar *a, const secp256k1_scalar *b, unsigned int shift);
 
-/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time.  Both *r and *a must be initialized.*/
 static void secp256k1_scalar_cmov(secp256k1_scalar *r, const secp256k1_scalar *a, int flag);
 
 #endif /* SECP256K1_SCALAR_H */
diff --git a/src/secp256k1.c b/src/secp256k1.c
index de66be5..2b2238b 100644
--- a/src/secp256k1.c
+++ b/src/secp256k1.c
@@ -468,7 +468,8 @@ const secp256k1_nonce_function secp256k1_nonce_function_rfc6979 = nonce_function
 const secp256k1_nonce_function secp256k1_nonce_function_default = nonce_function_rfc6979;
 
 int secp256k1_ecdsa_sign(const secp256k1_context* ctx, secp256k1_ecdsa_signature *signature, const unsigned char *msg32, const unsigned char *seckey, secp256k1_nonce_function noncefp, const void* noncedata) {
-    secp256k1_scalar r, s;
+    /* Default initialization here is important so we won't pass uninit values to the cmov in the end */
+    secp256k1_scalar r = secp256k1_scalar_zero, s = secp256k1_scalar_zero;
     secp256k1_scalar sec, non, msg;
     int ret = 0;
     int is_sec_valid;