diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h
index 5277f56d9..ee3743048 100644
--- a/include/mbedtls/bignum.h
+++ b/include/mbedtls/bignum.h
@@ -277,7 +277,7 @@ void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
  * \param Y        The MPI to be assigned from. This must point to an
  *                 initialized MPI.
  * \param assign   The condition deciding whether to perform the
- *                 assignment or not. Possible values:
+ *                 assignment or not. Must be either 0 or 1:
  *                 * \c 1: Perform the assignment `X = Y`.
  *                 * \c 0: Keep the original value of \p X.
  *
@@ -288,6 +288,10 @@ void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
  *                 information through branch prediction and/or memory access
  *                 patterns analysis).
  *
+ * \warning        If \p assign is neither 0 nor 1, the result of this function
+ *                 is indeterminate, and the resulting value in \p X might be
+ *                 neither its original value nor the value in \p Y.
+ *
  * \return         \c 0 if successful.
  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
  * \return         Another negative error code on other kinds of failure.
@@ -300,24 +304,28 @@ int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned
  *
  * \param X        The first MPI. This must be initialized.
  * \param Y        The second MPI. This must be initialized.
- * \param assign   The condition deciding whether to perform
- *                 the swap or not. Possible values:
+ * \param swap     The condition deciding whether to perform
+ *                 the swap or not. Must be either 0 or 1:
  *                 * \c 1: Swap the values of \p X and \p Y.
  *                 * \c 0: Keep the original values of \p X and \p Y.
  *
  * \note           This function is equivalent to
- *                      if( assign ) mbedtls_mpi_swap( X, Y );
+ *                      if( swap ) mbedtls_mpi_swap( X, Y );
  *                 except that it avoids leaking any information about whether
- *                 the assignment was done or not (the above code may leak
+ *                 the swap was done or not (the above code may leak
  *                 information through branch prediction and/or memory access
  *                 patterns analysis).
  *
+ * \warning        If \p swap is neither 0 nor 1, the result of this function
+ *                 is indeterminate, and both \p X and \p Y might end up with
+ *                 values different to either of the original ones.
+ *
  * \return         \c 0 if successful.
  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
  * \return         Another negative error code on other kinds of failure.
  *
  */
-int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign );
+int mbedtls_mpi_safe_cond_swap( mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap );
 
 /**
  * \brief          Store integer value in MPI.
diff --git a/library/constant_time.c b/library/constant_time.c
index 47e9b02d6..0dc723a61 100644
--- a/library/constant_time.c
+++ b/library/constant_time.c
@@ -272,7 +272,7 @@ unsigned mbedtls_ct_uint_if( unsigned condition,
  * \note if1 and if0 must be either 1 or -1, otherwise the result
  *       is undefined.
  *
- * \param condition     Condition to test.
+ * \param condition     Condition to test; must be either 0 or 1.
  * \param if1           The first sign; must be either +1 or -1.
  * \param if0           The second sign; must be either +1 or -1.
  *