diff --git a/.evergreen/linker_tests_deps/app/CMakeLists.txt b/.evergreen/linker_tests_deps/app/CMakeLists.txt
index 1a5abb1dd..9b9f907e3 100644
--- a/.evergreen/linker_tests_deps/app/CMakeLists.txt
+++ b/.evergreen/linker_tests_deps/app/CMakeLists.txt
@@ -1,4 +1,4 @@
-cmake_minimum_required (VERSION 3.5)
+cmake_minimum_required (VERSION 3.15...4.0)
 project (app C)
 add_executable (app app.c)
 find_package (bson-1.0 1.11 REQUIRED)
@@ -6,4 +6,4 @@ message ("--   libbson found version \"${bson-1.0_VERSION}\"")
 target_link_libraries (app PRIVATE mongo::bson_static)
 
 find_package (mongocrypt REQUIRED)
-target_link_libraries (app PRIVATE mongo::mongocrypt)
\ No newline at end of file
+target_link_libraries (app PRIVATE mongo::mongocrypt)
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 837ead98f..08b02fd82 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,4 +1,11 @@
 # ChangeLog
+
+## 1.16.0 (Unreleased)
+
+### Changed
+
+- Set CMake minimum required version to `3.15...4.0` (with maximum policy version set to `4.0`).
+
 ## 1.15.0
 
 ### New features
diff --git a/CMakeLists.txt b/CMakeLists.txt
index d6fc6c72e..449bcb9f2 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -1,15 +1,4 @@
-cmake_minimum_required (VERSION 3.12)
-
-# Preempt the MSVC_RUNTIME_LIBRARY properties
-if (POLICY CMP0091)
-   cmake_policy (SET CMP0091 NEW)
-elseif (DEFINED CMAKE_MSVC_RUNTIME_LIBRARY)
-   message (WARNING "The CMAKE_MSVC_RUNTIME_LIBRARY variable is set, but CMake is too old to understand it")
-endif ()
-
-if (POLICY CMP0135)
-   cmake_policy (SET CMP0135 NEW)
-endif ()
+cmake_minimum_required (VERSION 3.15...4.0)
 
 project (mongocrypt C)
 
@@ -27,20 +16,7 @@ option (ENABLE_BUILD_FOR_PPA "Maintainer-only option for preparing PPA build" OF
 option (ENABLE_ONLINE_TESTS "Enable online tests and the csfle utility. Requires libmongoc." ON)
 
 if (ENABLE_WINDOWS_STATIC_RUNTIME)
-   if (POLICY CMP0091)
-      # CMake 3.15 makes this trivial:
-      set (CMAKE_MSVC_RUNTIME_LIBRARY "MultiThreaded$<$<CONFIG:Debug>:Debug>")
-   else ()
-      # Fix it up the old-fashioned way
-      string (REPLACE "/MDd" "" CMAKE_C_FLAGS "${CMAKE_C_FLAGS}")
-      string (REPLACE "/MD" "" CMAKE_C_FLAGS_RELEASE "${CMAKE_C_FLAGS_RELEASE}")
-      string (REPLACE "/MDd" "" CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS}")
-      string (REPLACE "/MD" "" CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE}")
-      string (APPEND CMAKE_C_FLAGS_DEBUG " /MTd")
-      string (APPEND CMAKE_CXX_FLAGS_DEBUG " /MTd")
-      string (APPEND CMAKE_C_FLAGS_RELEASE " /MT")
-      string (APPEND CMAKE_CXX_FLAGS_RELEASE " /MT")
-   endif ()
+   set (CMAKE_MSVC_RUNTIME_LIBRARY "MultiThreaded$<$<CONFIG:Debug>:Debug>")
 endif ()
 
 list (APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
diff --git a/cmake/MongoC-Warnings.cmake b/cmake/MongoC-Warnings.cmake
index 4784c9330..eb104f482 100644
--- a/cmake/MongoC-Warnings.cmake
+++ b/cmake/MongoC-Warnings.cmake
@@ -42,14 +42,7 @@ function (mongoc_add_platform_compile_options)
    endforeach ()
 endfunction ()
 
-if (CMAKE_VERSION VERSION_LESS 3.3)
-   # On older CMake versions, we'll just always pass the warning options, even
-   # if the generate warnings for the C++ check file
-   set (is_c_lang "1")
-else ()
-   # $<COMPILE_LANGUAGE> is only valid in CMake 3.3+
-   set (is_c_lang "$<COMPILE_LANGUAGE:C>")
-endif ()
+set (is_c_lang "$<COMPILE_LANGUAGE:C>")
 
 # These below warnings should always be unconditional hard errors, as the code is
 # almost definitely broken
diff --git a/kms-message/CMakeLists.txt b/kms-message/CMakeLists.txt
index 6848e61f6..ff210d4fc 100644
--- a/kms-message/CMakeLists.txt
+++ b/kms-message/CMakeLists.txt
@@ -1,4 +1,4 @@
-cmake_minimum_required (VERSION 3.5)
+cmake_minimum_required (VERSION 3.15...4.0)
 project (kms_message
    VERSION 0.0.1
    LANGUAGES C
@@ -7,8 +7,7 @@ project (kms_message
 set (CMAKE_C_STANDARD 99)
 
 include (CheckCCompilerFlag)
-# All targets obey visibility, not just library targets.
-cmake_policy (SET CMP0063 NEW)
+
 set (CMAKE_C_VISIBILITY_PRESET hidden)
 set (KMS_MESSAGE_SOURCES
    src/kms_b64.c