diff --git a/CMakeLists.txt b/CMakeLists.txt
index 4ca8cbe8e3..fb30d69458 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -200,8 +200,8 @@ mark_as_advanced(
   CMAKE_SHARED_LINKER_FLAGS_COVERAGE
 )
 
+get_property(is_multi_config GLOBAL PROPERTY GENERATOR_IS_MULTI_CONFIG)
 if(PROJECT_IS_TOP_LEVEL)
-  get_property(is_multi_config GLOBAL PROPERTY GENERATOR_IS_MULTI_CONFIG)
   set(default_build_type "RelWithDebInfo")
   if(is_multi_config)
     set(CMAKE_CONFIGURATION_TYPES "${default_build_type}" "Release" "Debug" "MinSizeRel" "Coverage" CACHE STRING
@@ -311,10 +311,15 @@ message("Optional binaries:")
 message("  benchmark ........................... ${SECP256K1_BUILD_BENCHMARK}")
 message("  noverify_tests ...................... ${SECP256K1_BUILD_TESTS}")
 set(tests_status "${SECP256K1_BUILD_TESTS}")
-if(CMAKE_BUILD_TYPE STREQUAL "Coverage")
-  set(tests_status OFF)
+if(tests_status)
+  if(is_multi_config)
+    set(tests_status "${tests_status}, except for the 'Coverage' configuration")
+  elseif(CMAKE_BUILD_TYPE STREQUAL "Coverage")
+    set(tests_status OFF)
+  endif()
 endif()
 message("  tests ............................... ${tests_status}")
+unset(tests_status)
 message("  exhaustive tests .................... ${SECP256K1_BUILD_EXHAUSTIVE_TESTS}")
 message("  ctime_tests ......................... ${SECP256K1_BUILD_CTIME_TESTS}")
 message("  examples ............................ ${SECP256K1_BUILD_EXAMPLES}")
@@ -363,6 +368,14 @@ if(print_msan_notice)
     "  to avoid false positives in ctime_tests. Pass -DSECP256K1_BUILD_CTIME_TESTS=OFF to avoid this.\n"
   )
 endif()
+if($CACHE{SECP256K1_print_coverage_notice})
+  message(
+    "Note:\n"
+    "  CMake ${CMAKE_VERSION} does not support the '${CMAKE_GENERATOR}' generator fully. Consequently,\n"
+    "  the build system will still compile the 'tests' binary for the 'Coverage' configuration,\n"
+    "  which is meaningless.\n"
+  )
+endif()
 if(SECP256K1_EXPERIMENTAL)
   message(
     "  ******\n"
diff --git a/configure.ac b/configure.ac
index 6841543f59..a3a405793d 100644
--- a/configure.ac
+++ b/configure.ac
@@ -145,7 +145,7 @@ AC_ARG_ENABLE(benchmark,
     [SECP_SET_DEFAULT([enable_benchmark], [yes], [yes])])
 
 AC_ARG_ENABLE(coverage,
-    AS_HELP_STRING([--enable-coverage],[enable compiler flags to support kcov coverage analysis [default=no]]), [],
+    AS_HELP_STRING([--enable-coverage],[enable coverage analysis support [default=no]]), [],
     [SECP_SET_DEFAULT([enable_coverage], [no], [no])])
 
 AC_ARG_ENABLE(tests,
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 4cbaeb914d..c97b1e797d 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -88,12 +88,24 @@ if(SECP256K1_BUILD_TESTS)
   add_executable(noverify_tests tests.c)
   target_link_libraries(noverify_tests secp256k1_precomputed secp256k1_asm)
   add_test(NAME noverify_tests COMMAND noverify_tests)
-  if(NOT CMAKE_BUILD_TYPE STREQUAL "Coverage")
-    add_executable(tests tests.c)
-    target_compile_definitions(tests PRIVATE VERIFY)
-    target_link_libraries(tests secp256k1_precomputed secp256k1_asm)
-    add_test(NAME tests COMMAND tests)
+
+  add_executable(tests tests.c)
+  if(CMAKE_VERSION VERSION_GREATER_EQUAL 3.19)
+    set_target_properties(tests PROPERTIES EXCLUDE_FROM_ALL $<CONFIG:Coverage>)
+  else()
+    get_property(is_multi_config GLOBAL PROPERTY GENERATOR_IS_MULTI_CONFIG)
+    if(is_multi_config)
+      set(SECP256K1_print_coverage_notice YES CACHE INTERNAL "")
+    endif()
+  endif()
+  target_compile_definitions(tests PRIVATE VERIFY)
+  target_link_libraries(tests secp256k1_precomputed secp256k1_asm)
+  set(configs ${CMAKE_BUILD_TYPE} ${CMAKE_CONFIGURATION_TYPES})
+  list(REMOVE_ITEM configs Coverage)
+  if(configs)
+    add_test(NAME tests COMMAND tests CONFIGURATIONS ${configs})
   endif()
+  unset(configs)
 endif()
 
 if(SECP256K1_BUILD_EXHAUSTIVE_TESTS)