diff --git a/tools/objtool/Documentation/klp-test-design.txt b/tools/objtool/Documentation/klp-test-design.txt
index 67d20bf0dc10..2082c277197f 100644
--- a/tools/objtool/Documentation/klp-test-design.txt
+++ b/tools/objtool/Documentation/klp-test-design.txt
@@ -243,7 +243,17 @@ setting a cross compiler cannot produce one the host is unable to run.  ARCH
 selects both the objtool target and the directory of tests to run.
 
 clang needs telling, since it defaults to the host triple however it is
-invoked.  The fixtures include no kernel headers, so no sysroot is needed:
+invoked.  LLVM=1 with CROSS_COMPILE does that for you -- the --target= it
+derives is forwarded to the tests -- and the fixtures include no kernel
+headers, so no sysroot is needed:
+
+::
+
+    ARCH=x86_64 CROSS_COMPILE=x86_64-linux-gnu- LLVM=1 \
+            make -C tools/objtool tests
+
+Naming the compiler by hand works too, and is what to reach for when the
+target triple is not the one CROSS_COMPILE implies:
 
 ::
 
diff --git a/tools/objtool/Makefile b/tools/objtool/Makefile
index d3db9663ae1b..db99c4759b2c 100644
--- a/tools/objtool/Makefile
+++ b/tools/objtool/Makefile
@@ -153,8 +153,17 @@ clean: $(LIBSUBCMD)-clean
 mrproper: clean
 	$(call QUIET_CLEAN, objtool) $(RM) $(OBJTOOL)
 
+# The kernel's own Makefile sets OBJCOPY, to llvm-objcopy under LLVM and to
+# $(CROSS_COMPILE)objcopy otherwise; tools/scripts/Makefile.include names only
+# LLVM_OBJCOPY and leaves OBJCOPY unset.  Forwarding it unset would hand the
+# tests an empty string, and they would fall back to GNU objcopy even when
+# asked for an LLVM toolchain.
+OBJCOPY ?= $(if $(LLVM),$(LLVM_OBJCOPY),$(CROSS_COMPILE)objcopy)
+
 tests: $(OBJTOOL)
 	$(Q)OBJTOOL=$(abspath $(OBJTOOL)) ARCH=$(ARCH) CROSS_COMPILE=$(CROSS_COMPILE) \
+		CC='$(CC) $(CLANG_CROSS_FLAGS)' LD='$(LD)' \
+		READELF='$(READELF)' OBJCOPY='$(OBJCOPY)' \
 		KEEP=$(KEEP) $(srctree)/tools/objtool/tests/run-tests.sh
 
 FORCE: