diff --git a/CMakeLists.txt b/CMakeLists.txt
index 886d3879..8557c65b 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -503,13 +503,13 @@ endif()
 # Checks #
 ##########
 
-set(ADDITIONAL_SUPPORTED_CHECKS crc64 sha256)
+set(SUPPORTED_CHECKS crc32 crc64 sha256)
 
-set(ADDITIONAL_CHECK_TYPES "${ADDITIONAL_SUPPORTED_CHECKS}" CACHE STRING
-    "Additional check types to support (crc32 is always built)")
+set(XZ_CHECKS "${SUPPORTED_CHECKS}" CACHE STRING
+    "Check types to support (crc32 is always built)")
 
-foreach(CHECK IN LISTS ADDITIONAL_CHECK_TYPES)
-    if(NOT CHECK IN_LIST ADDITIONAL_SUPPORTED_CHECKS)
+foreach(CHECK IN LISTS XZ_CHECKS)
+    if(NOT CHECK IN_LIST SUPPORTED_CHECKS)
         message(FATAL_ERROR "'${CHECK}' is not a supported check type")
     endif()
 endforeach()
@@ -530,7 +530,7 @@ else()
     endif()
 endif()
 
-if("crc64" IN_LIST ADDITIONAL_CHECK_TYPES)
+if("crc64" IN_LIST XZ_CHECKS)
     add_compile_definitions("HAVE_CHECK_CRC64")
 
     if(XZ_SMALL)
@@ -550,7 +550,7 @@ if("crc64" IN_LIST ADDITIONAL_CHECK_TYPES)
     endif()
 endif()
 
-if("sha256" IN_LIST ADDITIONAL_CHECK_TYPES)
+if("sha256" IN_LIST XZ_CHECKS)
     add_compile_definitions("HAVE_CHECK_SHA256")
     target_sources(liblzma PRIVATE src/liblzma/check/sha256.c)
 endif()
diff --git a/tests/tests.cmake b/tests/tests.cmake
index 9778baee..1b30ddd4 100644
--- a/tests/tests.cmake
+++ b/tests/tests.cmake
@@ -108,17 +108,16 @@ if(BUILD_TESTING)
         set(HAVE_ALL_DECODERS OFF)
     endif()
 
-    set(ADDITIONAL_SUPPORTED_CHECKS_SORTED "${ADDITIONAL_SUPPORTED_CHECKS}")
-    list(SORT ADDITIONAL_SUPPORTED_CHECKS_SORTED)
+    set(SUPPORTED_CHECKS_SORTED "${SUPPORTED_CHECKS}")
+    list(SORT SUPPORTED_CHECKS_SORTED)
 
-    set(ADDITIONAL_CHECK_TYPES_SORTED "${ADDITIONAL_CHECK_TYPES}")
-    list(SORT ADDITIONAL_CHECK_TYPES_SORTED)
+    set(XZ_CHECKS_SORTED "${XZ_CHECKS}")
+    list(SORT XZ_CHECKS_SORTED)
 
-    if("${ADDITIONAL_SUPPORTED_CHECKS_SORTED}" STREQUAL
-        "${ADDITIONAL_CHECK_TYPES_SORTED}")
-        set(HAVE_ALL_CHECK_TYPES ON)
+    if("${SUPPORTED_CHECKS_SORTED}" STREQUAL "${XZ_CHECKS_SORTED}")
+        set(HAVE_ALL_CHECKS ON)
     else()
-        set(HAVE_ALL_CHECK_TYPES OFF)
+        set(HAVE_ALL_CHECKS OFF)
     endif()
 
     # test_scripts.sh only needs LZMA2 decoder and CRC32.
@@ -178,7 +177,7 @@ if(BUILD_TESTING)
 
     # test_files.sh decompresses files that use different filters and
     # check types so run it only if support for all of them has been enabled.
-    if(UNIX AND HAVE_ALL_DECODERS AND HAVE_ALL_CHECK_TYPES AND XZ_LZIP_DECODER)
+    if(UNIX AND HAVE_ALL_DECODERS AND HAVE_ALL_CHECKS AND XZ_LZIP_DECODER)
         # test_files.sh doesn't make any temporary files but it
         # must not be run at the top-level build directory because
         # it checks if ../config.h exists. We don't want to read