diff --git a/crypto/curve25519/curve25519.c b/crypto/curve25519/curve25519.c
index 17740b83e..6a0af2d9f 100644
--- a/crypto/curve25519/curve25519.c
+++ b/crypto/curve25519/curve25519.c
@@ -35,10 +35,6 @@
 // Various pre-computed constants.
 #include "./curve25519_tables.h"
 
-#if defined(OPENSSL_NO_ASM)
-#define FIAT_25519_NO_ASM
-#endif
-
 #if defined(BORINGSSL_CURVE25519_64BIT)
 #include "../../third_party/fiat/curve25519_64.h"
 #else
diff --git a/crypto/fipsmodule/bn/exponentiation.c b/crypto/fipsmodule/bn/exponentiation.c
index ad3770d6c..4ec9171e2 100644
--- a/crypto/fipsmodule/bn/exponentiation.c
+++ b/crypto/fipsmodule/bn/exponentiation.c
@@ -852,7 +852,11 @@ static int copy_from_prebuf(BIGNUM *b, int top, const BN_ULONG *table, int idx,
   OPENSSL_memset(b->d, 0, sizeof(BN_ULONG) * top);
   const int width = 1 << window;
   for (int i = 0; i < width; i++, table += top) {
-    BN_ULONG mask = constant_time_eq_int(i, idx);
+    // Use a value barrier to prevent Clang from adding a branch when |i != idx|
+    // and making this copy not constant time. Clang is still allowed to learn
+    // that |mask| is constant across the inner loop, so this won't inhibit any
+    // vectorization it might do.
+    BN_ULONG mask = value_barrier_w(constant_time_eq_int(i, idx));
     for (int j = 0; j < top; j++) {
       b->d[j] |= table[j] & mask;
     }
diff --git a/crypto/fipsmodule/ec/p256.c b/crypto/fipsmodule/ec/p256.c
index 816e6f1ad..bbbba948b 100644
--- a/crypto/fipsmodule/ec/p256.c
+++ b/crypto/fipsmodule/ec/p256.c
@@ -30,10 +30,6 @@
 #include "../delocate.h"
 #include "./internal.h"
 
-#if defined(OPENSSL_NO_ASM)
-#define FIAT_P256_NO_ASM
-#endif
-
 #if defined(BORINGSSL_HAS_UINT128)
 #define BORINGSSL_NISTP256_64BIT 1
 #include "../../../third_party/fiat/p256_64.h"
diff --git a/crypto/internal.h b/crypto/internal.h
index 9bbba9e5a..4060e4ce4 100644
--- a/crypto/internal.h
+++ b/crypto/internal.h
@@ -302,7 +302,7 @@ typedef uint32_t crypto_word_t;
 // always has the same output for a given input. This allows it to eliminate
 // dead code, move computations across loops, and vectorize.
 static inline crypto_word_t value_barrier_w(crypto_word_t a) {
-#if !defined(OPENSSL_NO_ASM) && (defined(__GNUC__) || defined(__clang__))
+#if defined(__GNUC__) || defined(__clang__)
   __asm__("" : "+r"(a) : /* no inputs */);
 #endif
   return a;
@@ -310,7 +310,7 @@ static inline crypto_word_t value_barrier_w(crypto_word_t a) {
 
 // value_barrier_u32 behaves like |value_barrier_w| but takes a |uint32_t|.
 static inline uint32_t value_barrier_u32(uint32_t a) {
-#if !defined(OPENSSL_NO_ASM) && (defined(__GNUC__) || defined(__clang__))
+#if defined(__GNUC__) || defined(__clang__)
   __asm__("" : "+r"(a) : /* no inputs */);
 #endif
   return a;
@@ -318,7 +318,7 @@ static inline uint32_t value_barrier_u32(uint32_t a) {
 
 // value_barrier_u64 behaves like |value_barrier_w| but takes a |uint64_t|.
 static inline uint64_t value_barrier_u64(uint64_t a) {
-#if !defined(OPENSSL_NO_ASM) && (defined(__GNUC__) || defined(__clang__))
+#if defined(__GNUC__) || defined(__clang__)
   __asm__("" : "+r"(a) : /* no inputs */);
 #endif
   return a;