diff --git a/crypto/fipsmodule/aes/aes_nohw.c b/crypto/fipsmodule/aes/aes_nohw.c
index 12cabcb..5bb24bc 100644
--- a/crypto/fipsmodule/aes/aes_nohw.c
+++ b/crypto/fipsmodule/aes/aes_nohw.c
@@ -18,6 +18,7 @@
 #include <string.h>
 
 #include "../../internal.h"
+#include "internal.h"
 
 #if defined(OPENSSL_SSE2)
 #include <emmintrin.h>
@@ -1181,29 +1182,27 @@
   aes_nohw_expand_round_keys(&sched, key);
 
   // Make |AES_NOHW_BATCH_SIZE| copies of |ivec|.
-  alignas(AES_NOHW_WORD_SIZE) union {
-    uint32_t u32[AES_NOHW_BATCH_SIZE * 4];
-    uint8_t u8[AES_NOHW_BATCH_SIZE * 16];
-  } ivs, enc_ivs;
+  alignas(AES_NOHW_WORD_SIZE) uint8_t ivs[AES_NOHW_BATCH_SIZE * 16];
+  alignas(AES_NOHW_WORD_SIZE) uint8_t enc_ivs[AES_NOHW_BATCH_SIZE * 16];
   for (size_t i = 0; i < AES_NOHW_BATCH_SIZE; i++) {
-    memcpy(ivs.u8 + 16 * i, ivec, 16);
+    memcpy(ivs + 16 * i, ivec, 16);
   }
 
-  uint32_t ctr = CRYPTO_bswap4(ivs.u32[3]);
+  uint32_t ctr = CRYPTO_load_u32_be(ivs + 12);
   for (;;) {
     // Update counters.
     for (size_t i = 0; i < AES_NOHW_BATCH_SIZE; i++) {
-      ivs.u32[4 * i + 3] = CRYPTO_bswap4(ctr + i);
+      CRYPTO_store_u32_be(ivs + 16 * i + 12, ctr + i);
     }
 
     size_t todo = blocks >= AES_NOHW_BATCH_SIZE ? AES_NOHW_BATCH_SIZE : blocks;
     AES_NOHW_BATCH batch;
-    aes_nohw_to_batch(&batch, ivs.u8, todo);
+    aes_nohw_to_batch(&batch, ivs, todo);
     aes_nohw_encrypt_batch(&sched, key->rounds, &batch);
-    aes_nohw_from_batch(enc_ivs.u8, todo, &batch);
+    aes_nohw_from_batch(enc_ivs, todo, &batch);
 
     for (size_t i = 0; i < todo; i++) {
-      aes_nohw_xor_block(out + 16 * i, in + 16 * i, enc_ivs.u8 + 16 * i);
+      aes_nohw_xor_block(out + 16 * i, in + 16 * i, enc_ivs + 16 * i);
     }
 
     blocks -= todo;
diff --git a/crypto/fipsmodule/aes/key_wrap.c b/crypto/fipsmodule/aes/key_wrap.c
index 0ec5f26..95b12d2 100644
--- a/crypto/fipsmodule/aes/key_wrap.c
+++ b/crypto/fipsmodule/aes/key_wrap.c
@@ -164,10 +164,8 @@
 int AES_wrap_key_padded(const AES_KEY *key, uint8_t *out, size_t *out_len,
                         size_t max_out, const uint8_t *in, size_t in_len) {
   // See https://tools.ietf.org/html/rfc5649#section-4.1
-  const uint32_t in_len32_be = CRYPTO_bswap4(in_len);
   const uint64_t in_len64 = in_len;
   const size_t padded_len = (in_len + 7) & ~7;
-
   *out_len = 0;
   if (in_len == 0 || in_len64 > 0xffffffffu || in_len + 7 < in_len ||
       padded_len + 8 < padded_len || max_out < padded_len + 8) {
@@ -176,7 +174,7 @@
 
   uint8_t block[AES_BLOCK_SIZE];
   memcpy(block, kPaddingConstant, sizeof(kPaddingConstant));
-  memcpy(block + 4, &in_len32_be, sizeof(in_len32_be));
+  CRYPTO_store_u32_be(block + 4, (uint32_t)in_len);
 
   if (in_len <= 8) {
     memset(block + 8, 0, 8);
@@ -226,9 +224,7 @@
   crypto_word_t ok = constant_time_eq_int(
       CRYPTO_memcmp(iv, kPaddingConstant, sizeof(kPaddingConstant)), 0);
 
-  uint32_t claimed_len32;
-  memcpy(&claimed_len32, iv + 4, sizeof(claimed_len32));
-  const size_t claimed_len = CRYPTO_bswap4(claimed_len32);
+  const size_t claimed_len = CRYPTO_load_u32_be(iv + 4);
   ok &= ~constant_time_is_zero_w(claimed_len);
   ok &= constant_time_eq_w((claimed_len - 1) >> 3, (in_len - 9) >> 3);
 
diff --git a/crypto/fipsmodule/cipher/e_aes.c b/crypto/fipsmodule/cipher/e_aes.c
index ad64a39..e94d59a 100644
--- a/crypto/fipsmodule/cipher/e_aes.c
+++ b/crypto/fipsmodule/cipher/e_aes.c
@@ -1297,12 +1297,9 @@
   }
 
   // The given nonces must be strictly monotonically increasing.
-  uint64_t given_counter;
-  OPENSSL_memcpy(&given_counter, nonce + nonce_len - sizeof(given_counter),
-                 sizeof(given_counter));
-  given_counter = CRYPTO_bswap8(given_counter);
-  if (given_counter == UINT64_MAX ||
-      given_counter < gcm_ctx->min_next_nonce) {
+  uint64_t given_counter =
+      CRYPTO_load_u64_be(nonce + nonce_len - sizeof(uint64_t));
+  if (given_counter == UINT64_MAX || given_counter < gcm_ctx->min_next_nonce) {
     OPENSSL_PUT_ERROR(CIPHER, CIPHER_R_INVALID_NONCE);
     return 0;
   }
@@ -1397,10 +1394,8 @@
   // The given nonces must be strictly monotonically increasing. See
   // https://tools.ietf.org/html/rfc8446#section-5.3 for details of the TLS 1.3
   // nonce construction.
-  uint64_t given_counter;
-  OPENSSL_memcpy(&given_counter, nonce + nonce_len - sizeof(given_counter),
-                 sizeof(given_counter));
-  given_counter = CRYPTO_bswap8(given_counter);
+  uint64_t given_counter =
+      CRYPTO_load_u64_be(nonce + nonce_len - sizeof(uint64_t));
 
   if (gcm_ctx->first) {
     // In the first call the sequence number will be zero and therefore the
diff --git a/crypto/fipsmodule/modes/cbc.c b/crypto/fipsmodule/modes/cbc.c
index 192580e..ac0cd42 100644
--- a/crypto/fipsmodule/modes/cbc.c
+++ b/crypto/fipsmodule/modes/cbc.c
@@ -116,11 +116,7 @@
   assert(inptr >= outptr || inptr + len <= outptr);
 
   size_t n;
-  union {
-    crypto_word_t t[16 / sizeof(crypto_word_t)];
-    uint8_t c[16];
-  } tmp;
-
+  alignas(16) uint8_t tmp[16];
   if ((inptr >= 32 && outptr <= inptr - 32) || inptr < outptr) {
     // If |out| is at least two blocks behind |in| or completely disjoint, there
     // is no need to decrypt to a temporary block.
@@ -144,10 +140,10 @@
                           "block cannot be evenly divided into words");
 
     while (len >= 16) {
-      (*block)(in, tmp.c, key);
+      (*block)(in, tmp, key);
       for (n = 0; n < 16; n += sizeof(crypto_word_t)) {
         crypto_word_t c = CRYPTO_load_word_le(in + n);
-        CRYPTO_store_word_le(out + n, tmp.t[n / sizeof(crypto_word_t)] ^
+        CRYPTO_store_word_le(out + n, CRYPTO_load_word_le(tmp + n) ^
                                           CRYPTO_load_word_le(ivec + n));
         CRYPTO_store_word_le(ivec + n, c);
       }
@@ -159,10 +155,10 @@
 
   while (len) {
     uint8_t c;
-    (*block)(in, tmp.c, key);
+    (*block)(in, tmp, key);
     for (n = 0; n < 16 && n < len; ++n) {
       c = in[n];
-      out[n] = tmp.c[n] ^ ivec[n];
+      out[n] = tmp[n] ^ ivec[n];
       ivec[n] = c;
     }
     if (len <= 16) {
diff --git a/crypto/fipsmodule/rand/ctrdrbg.c b/crypto/fipsmodule/rand/ctrdrbg.c
index 83e7f5b..3b21d76 100644
--- a/crypto/fipsmodule/rand/ctrdrbg.c
+++ b/crypto/fipsmodule/rand/ctrdrbg.c
@@ -59,7 +59,7 @@
   }
 
   drbg->ctr = aes_ctr_set_key(&drbg->ks, NULL, &drbg->block, seed_material, 32);
-  OPENSSL_memcpy(drbg->counter.bytes, seed_material + 32, 16);
+  OPENSSL_memcpy(drbg->counter, seed_material + 32, 16);
   drbg->reseed_counter = 1;
 
   return 1;
@@ -71,8 +71,8 @@
 // ctr_inc adds |n| to the last four bytes of |drbg->counter|, treated as a
 // big-endian number.
 static void ctr32_add(CTR_DRBG_STATE *drbg, uint32_t n) {
-  drbg->counter.words[3] =
-      CRYPTO_bswap4(CRYPTO_bswap4(drbg->counter.words[3]) + n);
+  uint32_t ctr = CRYPTO_load_u32_be(drbg->counter + 12);
+  CRYPTO_store_u32_be(drbg->counter + 12, ctr + n);
 }
 
 static int ctr_drbg_update(CTR_DRBG_STATE *drbg, const uint8_t *data,
@@ -87,7 +87,7 @@
   uint8_t temp[CTR_DRBG_ENTROPY_LEN];
   for (size_t i = 0; i < CTR_DRBG_ENTROPY_LEN; i += AES_BLOCK_SIZE) {
     ctr32_add(drbg, 1);
-    drbg->block(drbg->counter.bytes, temp + i, &drbg->ks);
+    drbg->block(drbg->counter, temp + i, &drbg->ks);
   }
 
   for (size_t i = 0; i < data_len; i++) {
@@ -95,7 +95,7 @@
   }
 
   drbg->ctr = aes_ctr_set_key(&drbg->ks, NULL, &drbg->block, temp, 32);
-  OPENSSL_memcpy(drbg->counter.bytes, temp + 32, 16);
+  OPENSSL_memcpy(drbg->counter, temp + 32, 16);
 
   return 1;
 }
@@ -167,12 +167,12 @@
     if (drbg->ctr) {
       OPENSSL_memset(out, 0, todo);
       ctr32_add(drbg, 1);
-      drbg->ctr(out, out, num_blocks, &drbg->ks, drbg->counter.bytes);
+      drbg->ctr(out, out, num_blocks, &drbg->ks, drbg->counter);
       ctr32_add(drbg, num_blocks - 1);
     } else {
       for (size_t i = 0; i < todo; i += AES_BLOCK_SIZE) {
         ctr32_add(drbg, 1);
-        drbg->block(drbg->counter.bytes, out + i, &drbg->ks);
+        drbg->block(drbg->counter, out + i, &drbg->ks);
       }
     }
 
@@ -183,7 +183,7 @@
   if (out_len > 0) {
     uint8_t block[AES_BLOCK_SIZE];
     ctr32_add(drbg, 1);
-    drbg->block(drbg->counter.bytes, block, &drbg->ks);
+    drbg->block(drbg->counter, block, &drbg->ks);
 
     OPENSSL_memcpy(out, block, out_len);
   }
diff --git a/crypto/fipsmodule/rand/internal.h b/crypto/fipsmodule/rand/internal.h
index eccf047..b0133a8 100644
--- a/crypto/fipsmodule/rand/internal.h
+++ b/crypto/fipsmodule/rand/internal.h
@@ -99,10 +99,7 @@
   AES_KEY ks;
   block128_f block;
   ctr128_f ctr;
-  union {
-    uint8_t bytes[16];
-    uint32_t words[4];
-  } counter;
+  uint8_t counter[16];
   uint64_t reseed_counter;
 } CTR_DRBG_STATE;