diff --git a/tools/build/make.py b/tools/build/make.py
index 7ae6a95e8c23..74454aa51b08 100755
--- a/tools/build/make.py
+++ b/tools/build/make.py
@@ -48,6 +48,24 @@
 from pathlib import Path
 
 
+# List of targets that are independent of TARGET/TARGET_ARCH and thus do not
+# need them to be set. Keep in the same order as Makefile documents them (if
+# they are documented).
+mach_indep_targets = [
+    "cleanuniverse",
+    "universe",
+    "universe-toolchain",
+    "tinderbox"
+    "worlds",
+    "kernels",
+    "kernel-toolchains",
+    "targets",
+    "toolchains",
+    "makeman",
+    "sysent",
+]
+
+
 def run(cmd, **kwargs):
     cmd = list(map(str, cmd))  # convert all Path objects to str
     debug("Running", cmd)
@@ -190,7 +208,7 @@ def default_cross_toolchain():
     new_env_vars = {}
     if not sys.platform.startswith("freebsd"):
         if not is_make_var_set("TARGET") or not is_make_var_set("TARGET_ARCH"):
-            if "universe" not in sys.argv and "tinderbox" not in sys.argv:
+            if not set(sys.argv).intersection(set(mach_indep_targets)):
                 sys.exit("TARGET= and TARGET_ARCH= must be set explicitly "
                          "when building on non-FreeBSD")
     if not parsed_args.bootstrap_toolchain: