diff --git a/include/mbedtls/base64.h b/include/mbedtls/base64.h
index 18e83120b..352c652db 100644
--- a/include/mbedtls/base64.h
+++ b/include/mbedtls/base64.h
@@ -24,7 +24,6 @@
 #define MBEDTLS_BASE64_H
 
 #include <stddef.h>
-#include <limits.h>
 
 #define MBEDTLS_ERR_BASE64_BUFFER_TOO_SMALL               -0x002A  /**< Output buffer too small. */
 #define MBEDTLS_ERR_BASE64_INVALID_CHARACTER              -0x002C  /**< Invalid character in input. */
@@ -46,7 +45,8 @@ extern "C" {
  *                 *olen is always updated to reflect the amount
  *                 of data that has (or would have) been written.
  *                 If that length cannot be represented, then no data is
- *                 written to the buffer and *olen is set to SIZE_T_MAX.
+ *                 written to the buffer and *olen is set to the maximum
+ *                 length representable as a size_t.
  *
  * \note           Call this function with dlen = 0 to obtain the
  *                 required buffer size in *olen
diff --git a/library/base64.c b/library/base64.c
index fc44c15ae..3432e5fcd 100644
--- a/library/base64.c
+++ b/library/base64.c
@@ -69,6 +69,8 @@ static const unsigned char base64_dec_map[128] =
      49,  50,  51, 127, 127, 127, 127, 127
 };
 
+#define BASE64_SIZE_T_MAX   ( (size_t) -1 ) /* SIZE_T_MAX is not standard */
+
 /*
  * Encode a buffer into base64 format
  */
@@ -87,9 +89,9 @@ int mbedtls_base64_encode( unsigned char *dst, size_t dlen, size_t *olen,
 
     n = slen / 3 + ( slen % 3 != 0 );
 
-    if( n > ( SIZE_T_MAX - 1 ) / 4 )
+    if( n > ( BASE64_SIZE_T_MAX - 1 ) / 4 )
     {
-        *olen = SIZE_T_MAX;
+        *olen = BASE64_SIZE_T_MAX;
         return( MBEDTLS_ERR_BASE64_BUFFER_TOO_SMALL );
     }
 
diff --git a/library/bignum.c b/library/bignum.c
index 280bbfd85..628a6eedd 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -38,7 +38,6 @@
 #include "mbedtls/bn_mul.h"
 
 #include <string.h>
-#include <limits.h>
 
 #if defined(MBEDTLS_PLATFORM_C)
 #include "mbedtls/platform.h"
@@ -59,6 +58,8 @@ static void mbedtls_zeroize( void *v, size_t n ) {
 #define biL    (ciL << 3)               /* bits  in limb  */
 #define biH    (ciL << 2)               /* half limb size */
 
+#define MPI_SIZE_T_MAX  ( (size_t) -1 ) /* SIZE_T_MAX is not standard */
+
 /*
  * Convert between bits/chars and number of limbs
  * Divide first in order to avoid potential overflows
@@ -411,7 +412,7 @@ int mbedtls_mpi_read_string( mbedtls_mpi *X, int radix, const char *s )
 
     if( radix == 16 )
     {
-        if( slen > SIZE_T_MAX >> 2 )
+        if( slen > MPI_SIZE_T_MAX >> 2 )
             return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
 
         n = BITS_TO_LIMBS( slen << 2 );