diff --git a/.ci/compute_projects.py b/.ci/compute_projects.py
index a4cfecf0cef90..d1d4770f48677 100644
--- a/.ci/compute_projects.py
+++ b/.ci/compute_projects.py
@@ -32,6 +32,7 @@
     "lld": {"llvm"},
     "mlir": {"llvm"},
     "polly": {"llvm"},
+    "libcxx": {"clang"},
 }
 
 # This mapping describes the additional projects that should be tested when a
@@ -67,6 +68,7 @@
         "libclc",
         "openmp",
     },
+    "libcxx": {"lldb"},
 }
 
 # This mapping describes runtimes that should be enabled for a specific project,
@@ -89,6 +91,7 @@
     "llvm": {"libcxx", "libcxxabi", "libunwind"},
     "clang": {"libcxx", "libcxxabi", "libunwind"},
     ".ci": {"libcxx", "libcxxabi", "libunwind"},
+    "libcxx": {"libcxx"},
 }
 
 EXCLUDE_LINUX = {
@@ -206,20 +209,19 @@ def _exclude_projects(current_projects: Set[str], platform: str) -> Set[str]:
 def _compute_projects_to_test(modified_projects: Set[str], platform: str) -> Set[str]:
     projects_to_test = set()
     for modified_project in modified_projects:
+        if modified_project in DEPENDENTS_TO_TEST:
+            for dependent_project in DEPENDENTS_TO_TEST[modified_project]:
+                if (
+                    platform == "Windows"
+                    and dependent_project in EXCLUDE_DEPENDENTS_WINDOWS
+                ):
+                    continue
+                projects_to_test.add(dependent_project)
         if modified_project in RUNTIMES:
             continue
         # Skip all projects where we cannot run tests.
         if modified_project in PROJECT_CHECK_TARGETS:
             projects_to_test.add(modified_project)
-        if modified_project not in DEPENDENTS_TO_TEST:
-            continue
-        for dependent_project in DEPENDENTS_TO_TEST[modified_project]:
-            if (
-                platform == "Windows"
-                and dependent_project in EXCLUDE_DEPENDENTS_WINDOWS
-            ):
-                continue
-            projects_to_test.add(dependent_project)
     projects_to_test = _exclude_projects(projects_to_test, platform)
     return projects_to_test
 
diff --git a/.ci/compute_projects_test.py b/.ci/compute_projects_test.py
index fe1bf07eae8ff..817ce22767df6 100644
--- a/.ci/compute_projects_test.py
+++ b/.ci/compute_projects_test.py
@@ -239,16 +239,6 @@ def test_top_level_file(self):
         self.assertEqual(env_variables["runtimes_check_targets"], "")
         self.assertEqual(env_variables["runtimes_check_targets_needs_reconfig"], "")
 
-    def test_exclude_libcxx_in_projects(self):
-        env_variables = compute_projects.get_env_variables(
-            ["libcxx/CMakeLists.txt"], "Linux"
-        )
-        self.assertEqual(env_variables["projects_to_build"], "")
-        self.assertEqual(env_variables["project_check_targets"], "")
-        self.assertEqual(env_variables["runtimes_to_build"], "")
-        self.assertEqual(env_variables["runtimes_check_targets"], "")
-        self.assertEqual(env_variables["runtimes_check_targets_needs_reconfig"], "")
-
     def test_include_libc_in_runtimes(self):
         env_variables = compute_projects.get_env_variables(
             ["libc/CMakeLists.txt"], "Linux"
@@ -437,6 +427,28 @@ def test_lit(self):
             "check-cxx check-cxxabi check-unwind",
         )
 
+    def test_libcxx_linux(self):
+        env_variables = compute_projects.get_env_variables(
+            ["libcxx/CMakeLists.txt"], "Linux"
+        )
+        self.assertEqual(env_variables["projects_to_build"], "clang;lldb;llvm")
+        self.assertEqual(env_variables["project_check_targets"], "check-lldb")
+        self.assertEqual(env_variables["runtimes_to_build"], "libcxx")
+        self.assertEqual(env_variables["runtimes_check_targets"], "")
+        self.assertEqual(
+            env_variables["runtimes_check_targets_needs_reconfig"], "check-cxx"
+        )
+
+    def test_libxx_windows(self):
+        env_variables = compute_projects.get_env_variables(
+            ["libcxx/CMakeLists.txt"], "Windows"
+        )
+        self.assertEqual(env_variables["projects_to_build"], "")
+        self.assertEqual(env_variables["project_check_targets"], "")
+        self.assertEqual(env_variables["runtimes_to_build"], "")
+        self.assertEqual(env_variables["runtimes_check_targets"], "")
+        self.assertEqual(env_variables["runtimes_check_targets_needs_reconfig"], "")
+
 
 if __name__ == "__main__":
     unittest.main()