diff --git a/cmake/emu/qemu.cmake b/cmake/emu/qemu.cmake
index 2b8ee3d8db3..b576a288fe4 100644
--- a/cmake/emu/qemu.cmake
+++ b/cmake/emu/qemu.cmake
@@ -252,7 +252,10 @@ if(NOT QEMU_PIPE)
   set(QEMU_PIPE_COMMENT "\nTo exit from QEMU enter: 'CTRL+a, x'\n")
 endif()
 
-if(CONFIG_SMP)
+# Don't just test CONFIG_SMP, there is at least one test of the lower
+# level multiprocessor API that wants an auxiliary CPU but doesn't
+# want SMP using it.
+if(NOT CONFIG_MP_NUM_CPUS MATCHES "1")
   list(APPEND QEMU_SMP_FLAGS -smp cpus=${CONFIG_MP_NUM_CPUS})
 endif()
 
diff --git a/tests/kernel/mp/prj.conf b/tests/kernel/mp/prj.conf
index 9467c292689..5b0d7a6bdea 100644
--- a/tests/kernel/mp/prj.conf
+++ b/tests/kernel/mp/prj.conf
@@ -1 +1,2 @@
 CONFIG_ZTEST=y
+CONFIG_SMP=n
diff --git a/tests/kernel/mp/src/main.c b/tests/kernel/mp/src/main.c
index d95cec9907d..e6886b8de9a 100644
--- a/tests/kernel/mp/src/main.c
+++ b/tests/kernel/mp/src/main.c
@@ -9,6 +9,12 @@
 #include <ztest.h>
 #include <kernel.h>
 
+#ifdef CONFIG_SMP
+#error Cannot test MP API if SMP is using the CPUs
+#endif
+
+BUILD_ASSERT(CONFIG_MP_NUM_CPUS > 1);
+
 #define CPU1_STACK_SIZE 1024
 
 K_THREAD_STACK_DEFINE(cpu1_stack, CPU1_STACK_SIZE);
@@ -29,7 +35,8 @@ volatile int cpu_running;
  */
 void cpu1_fn(int key, void *arg)
 {
-	zassert_true(key, "bad irq key");
+	ARG_UNUSED(key);
+
 	zassert_true(arg == &cpu_arg && *(int *)arg == 12345, "wrong arg");
 
 	cpu_running = 1;
diff --git a/tests/kernel/mp/testcase.yaml b/tests/kernel/mp/testcase.yaml
index 09c24b2220a..c465c3d89ed 100644
--- a/tests/kernel/mp/testcase.yaml
+++ b/tests/kernel/mp/testcase.yaml
@@ -1,3 +1,4 @@
 tests:
   kernel.multiprocessing:
-    platform_whitelist: esp32
+    # Doesn't currently work on ARC, see #19599
+    filter: (CONFIG_MP_NUM_CPUS > 1) and not CONFIG_ARC