diff --git a/CMakeLists.txt b/CMakeLists.txt
index a5199e100a7f..a45e7fc13011 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,10 +1,8 @@
-cmake_minimum_required(VERSION 3.1.0)
+cmake_minimum_required(VERSION 3.1...3.18)
 
-# Use newer policies if available, up to most recent tested version of CMake.
-if(${CMAKE_VERSION} VERSION_LESS 3.11)
+# Fallback for using newer policies on CMake <3.12.
+if(${CMAKE_VERSION} VERSION_LESS 3.12)
   cmake_policy(VERSION ${CMAKE_MAJOR_VERSION}.${CMAKE_MINOR_VERSION})
-else()
-  cmake_policy(VERSION 3.11)
 endif()
 
 # Determine if fmt is built as a subproject (using add_subdirectory)
diff --git a/test/add-subdirectory-test/CMakeLists.txt b/test/add-subdirectory-test/CMakeLists.txt
index db7054bd8f99..9cc4b0e97fe8 100644
--- a/test/add-subdirectory-test/CMakeLists.txt
+++ b/test/add-subdirectory-test/CMakeLists.txt
@@ -1,4 +1,4 @@
-cmake_minimum_required(VERSION 3.1.0)
+cmake_minimum_required(VERSION 3.1...3.18)
 
 project(fmt-test)
 
diff --git a/test/compile-error-test/CMakeLists.txt b/test/compile-error-test/CMakeLists.txt
index 75a0c5a5e5e4..8202f279434e 100644
--- a/test/compile-error-test/CMakeLists.txt
+++ b/test/compile-error-test/CMakeLists.txt
@@ -1,6 +1,6 @@
 # Test if compile errors are produced where necessary.
 
-cmake_minimum_required(VERSION 3.1.0)
+cmake_minimum_required(VERSION 3.1...3.18)
 
 include(CheckCXXSourceCompiles)
 include(CheckCXXCompilerFlag)
diff --git a/test/find-package-test/CMakeLists.txt b/test/find-package-test/CMakeLists.txt
index 513575570bb7..93d686e64335 100644
--- a/test/find-package-test/CMakeLists.txt
+++ b/test/find-package-test/CMakeLists.txt
@@ -1,4 +1,4 @@
-cmake_minimum_required(VERSION 3.1.0)
+cmake_minimum_required(VERSION 3.1...3.18)
 
 project(fmt-test)