diff --git a/math/test-fesetexcept-traps.c b/math/test-fesetexcept-traps.c
index 96f6c4752f..8a5c0bca80 100644
--- a/math/test-fesetexcept-traps.c
+++ b/math/test-fesetexcept-traps.c
@@ -19,6 +19,7 @@
 #include <fenv.h>
 #include <stdio.h>
 #include <math-tests.h>
+#include <math-barriers.h>
 
 static int
 do_test (void)
@@ -41,8 +42,28 @@ do_test (void)
 
   /* Verify fesetexcept does not cause exception traps.  For architectures
      where setting the exception might result in traps the function should
-     return a nonzero value.  */
-  ret = fesetexcept (FE_ALL_EXCEPT);
+     return a nonzero value.
+     Also check if the function does not alter the exception mask.  */
+  {
+    int exc_before = fegetexcept ();
+    ret = fesetexcept (FE_ALL_EXCEPT);
+    int exc_after = fegetexcept ();
+    if (exc_before != exc_after)
+      {
+	puts ("fesetexcept (FE_ALL_EXCEPT) changed the exceptions mask");
+	return 1;
+      }
+  }
+
+  /* Execute some floating-point operations, since on some CPUs exceptions
+     triggers a trap only at the next floating-point instruction.  */
+  volatile double a = 1.0;
+  volatile double b = a + a;
+  math_force_eval (b);
+  volatile long double al = 1.0L;
+  volatile long double bl = al + al;
+  math_force_eval (bl);
+
   if (ret == 0)
     puts ("fesetexcept (FE_ALL_EXCEPT) succeeded");
   else if (!EXCEPTION_SET_FORCES_TRAP)
@@ -61,5 +82,4 @@ do_test (void)
   return result;
 }
 
-#define TEST_FUNCTION do_test ()
-#include "../test-skeleton.c"
+#include <support/test-driver.c>
diff --git a/sysdeps/i386/fpu/fesetexcept.c b/sysdeps/i386/fpu/fesetexcept.c
index 18949e982a..2e9580207c 100644
--- a/sysdeps/i386/fpu/fesetexcept.c
+++ b/sysdeps/i386/fpu/fesetexcept.c
@@ -17,15 +17,53 @@
    <https://www.gnu.org/licenses/>.  */
 
 #include <fenv.h>
+#include <ldsodefs.h>
 
 int
 fesetexcept (int excepts)
 {
-  fenv_t temp;
+  /* The flags can be set in the 387 unit or in the SSE unit.  To set a flag,
+     it is sufficient to do it in the SSE unit, because that is guaranteed to
+     not trap.  However, on i386 CPUs that have only a 387 unit, set the flags
+     in the 387, as long as this cannot trap.  */
 
-  __asm__ ("fnstenv %0" : "=m" (*&temp));
-  temp.__status_word |= excepts & FE_ALL_EXCEPT;
-  __asm__ ("fldenv %0" : : "m" (*&temp));
+  excepts &= FE_ALL_EXCEPT;
+
+  if (CPU_FEATURE_USABLE (SSE))
+    {
+      /* And now similarly for SSE.  */
+      unsigned int mxcsr;
+      __asm__ ("stmxcsr %0" : "=m" (*&mxcsr));
+
+      /* Set relevant flags.  */
+      mxcsr |= excepts;
+
+      /* Put the new data in effect.  */
+      __asm__ ("ldmxcsr %0" : : "m" (*&mxcsr));
+    }
+  else
+    {
+      fenv_t temp;
+
+      /* Note: fnstenv masks all floating-point exceptions until the fldenv
+	 or fldcw below.  */
+      __asm__ ("fnstenv %0" : "=m" (*&temp));
+
+      /* Set relevant flags.  */
+      temp.__status_word |= excepts;
+
+      if ((~temp.__control_word) & excepts)
+	{
+	  /* Setting the exception flags may trigger a trap (at the next
+	     floating-point instruction, but that does not matter).
+	     ISO C23 (7.6.4.4) does not allow it.  */
+	  __asm__ volatile ("fldcw %0" : : "m" (*&temp.__control_word));
+	  return -1;
+	}
+
+      /* Store the new status word (along with the rest of the environment).  */
+      __asm__ ("fldenv %0" : : "m" (*&temp));
+    }
 
   return 0;
 }
diff --git a/sysdeps/i386/fpu/math-tests-trap-force.h b/sysdeps/i386/fpu/math-tests-trap-force.h
new file mode 100644
index 0000000000..f41e1ffc2d
--- /dev/null
+++ b/sysdeps/i386/fpu/math-tests-trap-force.h
@@ -0,0 +1,29 @@
+/* Configuration for math tests: support for setting exception flags
+   without causing enabled traps.  i686 version.
+   Copyright (C) 2023 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public
+   License as published by the Free Software Foundation; either
+   version 2.1 of the License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; if not, see
+   <https://www.gnu.org/licenses/>.  */
+
+#ifndef I386_FPU_MATH_TESTS_TRAP_FORCE_H
+#define I386_FPU_MATH_TESTS_TRAP_FORCE_H 1
+
+#include <cpu-features.h>
+
+/* Setting exception flags in FPU Status Register results in enabled traps for
+   those exceptions being taken.  */
+#define EXCEPTION_SET_FORCES_TRAP !CPU_FEATURE_USABLE (SSE)
+
+#endif /* math-tests-trap-force.h.  */
diff --git a/sysdeps/x86/fpu/test-fenv-sse-2.c b/sysdeps/x86/fpu/test-fenv-sse-2.c
index f3e820b6ed..7a0503790f 100644
--- a/sysdeps/x86/fpu/test-fenv-sse-2.c
+++ b/sysdeps/x86/fpu/test-fenv-sse-2.c
@@ -22,17 +22,8 @@
 #include <stdbool.h>
 #include <stdint.h>
 #include <stdio.h>
-
-static bool
-have_sse2 (void)
-{
-  unsigned int eax, ebx, ecx, edx;
-
-  if (!__get_cpuid (1, &eax, &ebx, &ecx, &edx))
-    return false;
-
-  return (edx & bit_SSE2) != 0;
-}
+#include <cpu-features.h>
+#include <support/check.h>
 
 static uint32_t
 get_sse_mxcsr (void)
@@ -164,13 +155,9 @@ sse_tests (void)
 static int
 do_test (void)
 {
-  if (!have_sse2 ())
-    {
-      puts ("CPU does not support SSE2, cannot test");
-      return 0;
-    }
+  if (!CPU_FEATURE_USABLE (SSE2))
+    FAIL_UNSUPPORTED ("CPU does not support SSE2");
   return sse_tests ();
 }
 
-#define TEST_FUNCTION do_test ()
-#include <test-skeleton.c>
+#include <support/test-driver.c>
