diff --git a/CMakeLists.txt b/CMakeLists.txt
index 2d860d4a8b..a2fcf2e372 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,7 +1,7 @@
 # Distributed under the OSI-approved BSD 3-Clause License.  See accompanying
 # file Copyright.txt or https://cmake.org/licensing for details.
 
-cmake_minimum_required(VERSION 3.1...3.15 FATAL_ERROR)
+cmake_minimum_required(VERSION 3.1...3.18 FATAL_ERROR)
 set(CMAKE_USER_MAKE_RULES_OVERRIDE_C ${CMAKE_CURRENT_SOURCE_DIR}/Source/Modules/OverrideC.cmake)
 set(CMAKE_USER_MAKE_RULES_OVERRIDE_CXX ${CMAKE_CURRENT_SOURCE_DIR}/Source/Modules/OverrideCXX.cmake)
 project(CMake)
diff --git a/Help/dev/maint.rst b/Help/dev/maint.rst
index 75d685c61f..664b7a409f 100644
--- a/Help/dev/maint.rst
+++ b/Help/dev/maint.rst
@@ -357,3 +357,13 @@ policies added for that version.  Commit with a message such as::
   The files generatd by `install(EXPORT)` and `export()` commands
   are known to work with policies as of CMake $prev, so enable them
   in sufficiently new CMake versions.
+
+Update the ``cmake_minimum_required`` version range in CMake itself:
+
+* ``CMakeLists.txt``
+* ``Utilities/Doxygen/CMakeLists.txt``
+* ``Utilities/Sphinx/CMakeLists.txt``
+
+to end in the previous release.  Commit with a message such as::
+
+  Configure CMake itself with policies through CMake $prev
diff --git a/Source/cmExportFileGenerator.cxx b/Source/cmExportFileGenerator.cxx
index cbae4e59ab..a853bb18d7 100644
--- a/Source/cmExportFileGenerator.cxx
+++ b/Source/cmExportFileGenerator.cxx
@@ -924,13 +924,13 @@ void cmExportFileGenerator::GeneratePolicyHeaderCode(std::ostream& os)
 
   // Isolate the file policy level.
   // Support CMake versions as far back as 2.6 but also support using NEW
-  // policy settings for up to CMake 3.17 (this upper limit may be reviewed
+  // policy settings for up to CMake 3.18 (this upper limit may be reviewed
   // and increased from time to time). This reduces the opportunity for CMake
   // warnings when an older export file is later used with newer CMake
   // versions.
   /* clang-format off */
   os << "cmake_policy(PUSH)\n"
-     << "cmake_policy(VERSION 2.6...3.17)\n";
+     << "cmake_policy(VERSION 2.6...3.18)\n";
   /* clang-format on */
 }
 
diff --git a/Source/cmMakefile.cxx b/Source/cmMakefile.cxx
index 9286e93c8e..c366b489af 100644
--- a/Source/cmMakefile.cxx
+++ b/Source/cmMakefile.cxx
@@ -4427,7 +4427,7 @@ bool cmMakefile::SetPolicy(cmPolicies::PolicyID id,
 
   // Deprecate old policies, especially those that require a lot
   // of code to maintain the old behavior.
-  if (status == cmPolicies::OLD && id <= cmPolicies::CMP0072 &&
+  if (status == cmPolicies::OLD && id <= cmPolicies::CMP0075 &&
       !(this->GetCMakeInstance()->GetIsInTryCompile() &&
         (
           // Policies set by cmCoreTryCompile::TryCompileCode.
diff --git a/Tests/RunCMake/CheckModules/CMP0075-stderr.txt b/Tests/RunCMake/CheckModules/CMP0075-stderr.txt
index 960fe9444c..97833f582f 100644
--- a/Tests/RunCMake/CheckModules/CMP0075-stderr.txt
+++ b/Tests/RunCMake/CheckModules/CMP0075-stderr.txt
@@ -47,4 +47,15 @@ CMake Warning \(dev\) at [^
 Call Stack \(most recent call first\):
   CMP0075.cmake:41 \(check_include_files\)
   CMakeLists.txt:[0-9]+ \(include\)
-This warning is for project developers.  Use -Wno-dev to suppress it.$
+This warning is for project developers.  Use -Wno-dev to suppress it.
++
+CMake Deprecation Warning at CMP0075.cmake:[0-9]+ \(cmake_policy\):
+  The OLD behavior for policy CMP0075 will be removed from a future version
+  of CMake.
+
+  The cmake-policies\(7\) manual explains that the OLD behaviors of all
+  policies are deprecated and that a policy should be set to OLD only under
+  specific short-term circumstances.  Projects should be ported to the NEW
+  behavior and not rely on setting a policy to OLD.
+Call Stack \(most recent call first\):
+  CMakeLists.txt:[0-9]+ \(include\)$
diff --git a/Tests/RunCMake/add_library/CMP0073-stderr.txt b/Tests/RunCMake/add_library/CMP0073-stderr.txt
new file mode 100644
index 0000000000..7f43fd7408
--- /dev/null
+++ b/Tests/RunCMake/add_library/CMP0073-stderr.txt
@@ -0,0 +1,10 @@
+^CMake Deprecation Warning at CMP0073.cmake:[0-9]+ \(cmake_policy\):
+  The OLD behavior for policy CMP0073 will be removed from a future version
+  of CMake.
+
+  The cmake-policies\(7\) manual explains that the OLD behaviors of all
+  policies are deprecated and that a policy should be set to OLD only under
+  specific short-term circumstances.  Projects should be ported to the NEW
+  behavior and not rely on setting a policy to OLD.
+Call Stack \(most recent call first\):
+  CMakeLists.txt:[0-9]+ \(include\)$
diff --git a/Utilities/Doxygen/CMakeLists.txt b/Utilities/Doxygen/CMakeLists.txt
index 5bf13f3c9b..a880f7a81b 100644
--- a/Utilities/Doxygen/CMakeLists.txt
+++ b/Utilities/Doxygen/CMakeLists.txt
@@ -3,7 +3,7 @@
 
 if(NOT CMake_SOURCE_DIR)
   set(CMakeDeveloperReference_STANDALONE 1)
-  cmake_minimum_required(VERSION 3.1...3.15 FATAL_ERROR)
+  cmake_minimum_required(VERSION 3.1...3.18 FATAL_ERROR)
   get_filename_component(tmp "${CMAKE_CURRENT_SOURCE_DIR}" PATH)
   get_filename_component(CMake_SOURCE_DIR "${tmp}" PATH)
   include(${CMake_SOURCE_DIR}/Modules/CTestUseLaunchers.cmake)
diff --git a/Utilities/Sphinx/CMakeLists.txt b/Utilities/Sphinx/CMakeLists.txt
index e5be43ad89..f989907b40 100644
--- a/Utilities/Sphinx/CMakeLists.txt
+++ b/Utilities/Sphinx/CMakeLists.txt
@@ -3,7 +3,7 @@
 
 if(NOT CMake_SOURCE_DIR)
   set(CMakeHelp_STANDALONE 1)
-  cmake_minimum_required(VERSION 3.1...3.15 FATAL_ERROR)
+  cmake_minimum_required(VERSION 3.1...3.18 FATAL_ERROR)
   get_filename_component(tmp "${CMAKE_CURRENT_SOURCE_DIR}" PATH)
   get_filename_component(CMake_SOURCE_DIR "${tmp}" PATH)
   include(${CMake_SOURCE_DIR}/Modules/CTestUseLaunchers.cmake)