diff --git a/library/bignum.c b/library/bignum.c
index 54ab7e3ec..e9c3867a6 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -552,15 +552,20 @@ int mbedtls_mpi_write_string( const mbedtls_mpi *X, int radix,
     if( radix < 2 || radix > 16 )
         return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
 
-    n = mbedtls_mpi_bitlen( X );
-    if( radix >=  4 ) n >>= 1;
-    if( radix >= 16 ) n >>= 1;
-    /*
-     * Round up the buffer length to an even value to ensure that there is
-     * enough room for hexadecimal values that can be represented in an odd
-     * number of digits.
-     */
-    n += 3 + ( ( n + 1 ) & 1 );
+    n = mbedtls_mpi_bitlen( X ); /* Number of bits necessary to present `n`. */
+    if( radix >=  4 ) n >>= 1;   /* Number of 4-adic digits necessary to present
+                                  * `n`. If radix > 4, this might be a strict
+                                  * overapproximation of the number of
+                                  * radix-adic digits needed to present `n`. */
+    if( radix >= 16 ) n >>= 1;   /* Number of hexadecimal digits necessary to
+                                  * present `n`. */
+
+    n += 1; /* NULL termination */
+    n += 1; /* Compensate for the divisions above, which round down `n`
+             * in case it's not even. */
+    n += 1; /* Potential '-'-sign. */
+    n += ( n & 1 ); /* Make n even to have enough space for hexadecimal writing,
+                     * which always uses an even number of hex-digits. */
 
     if( buflen < n )
     {