diff --git a/Kernel_d/doc/Kernel_d/CGAL/Epick_d.h b/Kernel_d/doc/Kernel_d/CGAL/Epick_d.h
index 314c8a421c8..4230517c605 100644
--- a/Kernel_d/doc/Kernel_d/CGAL/Epick_d.h
+++ b/Kernel_d/doc/Kernel_d/CGAL/Epick_d.h
@@ -9,8 +9,9 @@ geometric objects. The parameter `Dimension` is the dimension of the
 ambient Euclidean space. It may be either `Dimension_tag<d>` or
 `Dynamic_dimension_tag`. It supports construction of points from `double`
 %Cartesian coordinates. It provides exact geometric predicates, but
-inexact geometric constructions. The geometric predicates are made exact
-without sacrificing speed thanks to the use of filters.
+the geometric constructions are not guaranteed to be exact. The geometric
+predicates are made exact without sacrificing speed thanks to the use of
+filters.
 
 This kernel is default constructible and copyable. It does not carry any
 state so it is possible to use objects created by one instance with
@@ -40,7 +41,9 @@ represents a point in the Euclidean space
 */
 class Point_d {
 public:
-/*! introduces a point with coordinates (x0, x1, ...). */
+/*! introduces a point with coordinates (x0, x1, ...) where the number of
+    coordinates matches the dimension.
+    \pre `Dimension` is a fixed dimension, not `Dynamic_dimension_tag` */
 Point_d(double x0, double x1, ...);
 
 /*! returns the i'th coordinate of a point.
diff --git a/Kernel_d/doc/Kernel_d/Kernel_d.txt b/Kernel_d/doc/Kernel_d/Kernel_d.txt
index 4a30f145d91..11abcacbc37 100644
--- a/Kernel_d/doc/Kernel_d/Kernel_d.txt
+++ b/Kernel_d/doc/Kernel_d/Kernel_d.txt
@@ -211,7 +211,8 @@ The kernel `Epick_d<Dimension>`, short for Exact Predicates Inexact
 Constructions Kernel is a kernel particularly useful when the dimension of
 the space is known at compile-time. It uses a Cartesian representation and
 supports construction of points from `double` coordinates. It provides exact
-geometric predicates, but inexact geometric constructions.
+geometric predicates, but the geometric constructions are not guaranteed to
+be exact.
 
 Note that it provides few interfaces in addition to those documented in the
 `Kernel_d` concept. In particular, the type of a point is only available as