diff --git a/Regression/bz580078-valgrind-aborts-with-vex-x86-IR-unhandled-instruction-bytes/main.fmf b/Regression/bz580078-valgrind-aborts-with-vex-x86-IR-unhandled-instruction-bytes/main.fmf
index 3844c59..e488ec0 100644
--- a/Regression/bz580078-valgrind-aborts-with-vex-x86-IR-unhandled-instruction-bytes/main.fmf
+++ b/Regression/bz580078-valgrind-aborts-with-vex-x86-IR-unhandled-instruction-bytes/main.fmf
@@ -45,6 +45,10 @@ adjust:
   - enabled: false
     when: arch != x86_64
 
+  # No i686 in RHEL-10+
+  - enabled: false
+    when: distro >= rhel-10
+
   # Testing farm does not support installing i686 packages in bodhi update testing,
   # so we disable this test there until that capacity is implemented.
   - enabled: false
diff --git a/Sanity/32bit-on-64bit-os/main.fmf b/Sanity/32bit-on-64bit-os/main.fmf
index 1b41f20..af58f83 100644
--- a/Sanity/32bit-on-64bit-os/main.fmf
+++ b/Sanity/32bit-on-64bit-os/main.fmf
@@ -26,6 +26,10 @@ adjust:
   - enabled: false
     when: arch != x86_64
 
+  # No i686 in RHEL-10+
+  - enabled: false
+    when: distro >= rhel-10
+
   # Testing farm does not support installing i686 packages in bodhi update testing,
   # so we disable this test there until that capacity is implemented.
   - enabled: false