diff --git a/test/blackbox-tests/gen_tests.ml b/test/blackbox-tests/gen_tests.ml
index 2abdbc9f..3ecc6856 100644
--- a/test/blackbox-tests/gen_tests.ml
+++ b/test/blackbox-tests/gen_tests.ml
@@ -95,7 +95,7 @@ let exclusions =
   ; make "multiple-private-libs"  ~skip_ocaml:"4.02.3"
   ; make "ppx-rewriter" ~skip_ocaml:"4.02.3" ~external_deps:true
   ; make "odoc-unique-mlds" ~skip_ocaml:"4.02.3" ~external_deps:true
-  ; make "output-obj" ~skip_platforms:[Mac; Win]
+  ; make "output-obj" ~skip_platforms:[Mac; Win] ~skip_ocaml:"<4.06.0"
   ; make "github644" ~external_deps:true
   ; make "private-public-overlap" ~external_deps:true
   ; make "reason" ~enabled:false
diff --git a/test/blackbox-tests/jbuild.inc b/test/blackbox-tests/jbuild.inc
index 8de03d72..c7afa078 100644
--- a/test/blackbox-tests/jbuild.inc
+++ b/test/blackbox-tests/jbuild.inc
@@ -329,7 +329,14 @@
    (chdir
     test-cases/output-obj
     (progn
-     (run ${exe:cram.exe} -skip-platforms macosx,win -test run.t)
+     (run
+      ${exe:cram.exe}
+      -skip-versions
+      <4.06.0
+      -skip-platforms
+      macosx,win
+      -test
+      run.t)
      (diff? run.t run.t.corrected))))))
 
 (alias