diff --git a/scripts/test.py b/scripts/test.py
index 8d9832e99..ee4b53bbe 100755
--- a/scripts/test.py
+++ b/scripts/test.py
@@ -927,9 +927,12 @@ def cibuildwheel(
     # will notice that the wheel we built above supports all versions of
     # Python, so will not actually do any builds here.
     #
-    env_extra['CIBW_BUILD'] = CIBW_BUILD
-    run(f'cd {pymupdf_dir} && cibuildwheel{cibw_pyodide_args}', env_extra=env_extra)
-    run(f'ls -ld {pymupdf_dir}/wheelhouse/*')
+    # We only do this if there are more than one Python versions. This still
+    # duplicates the testing of the first python version.
+    if len(CIBW_BUILD.split()) > 1:
+        env_extra['CIBW_BUILD'] = CIBW_BUILD
+        run(f'cd {pymupdf_dir} && cibuildwheel{cibw_pyodide_args}', env_extra=env_extra)
+        run(f'ls -ld {pymupdf_dir}/wheelhouse/*')
 
 
 def cibw_do_test_project(env_extra, CIBW_BUILD, cibw_pyodide, cibw_pyodide_args):
diff --git a/tests/conftest.py b/tests/conftest.py
index e1d02297a..06af5b7aa 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -77,11 +77,25 @@ def get_members(a):
     # Allow post-test checking that pymupdf._globals has not changed.
     _globals_pre = get_members(pymupdf._globals)
     
+    testsfailed_before = request.session.testsfailed
+    
     # Run the test.
     rep = yield
     
     sys.stdout.flush()
     
+    # This seems the only way for us to tell that a test has failed. In
+    # particular, <rep> is always None. We're implicitly relying on tests not
+    # being run in parallel.
+    #
+    failed = request.session.testsfailed - testsfailed_before
+    assert failed in (0, 1)
+    
+    if failed:
+        # Do not check post-test conditions if the test as failed. This avoids
+        # additional confusing `ERROR` status for failed tests.
+        return
+    
     # Test has run; check it did not create any MuPDF warnings etc.
     wt = pymupdf.TOOLS.mupdf_warnings()
     if not hasattr(pymupdf, 'mupdf'):
diff --git a/tests/test_tesseract.py b/tests/test_tesseract.py
index a36120cce..7650e8381 100644
--- a/tests/test_tesseract.py
+++ b/tests/test_tesseract.py
@@ -15,10 +15,6 @@ def test_tesseract():
     But if TESSDATA_PREFIX is set in the environment, we assert that
     FzPage.get_textpage_ocr() succeeds.
     '''
-    if os.environ.get('PYODIDE_ROOT'):
-        print('test_tesseract(): not running on Pyodide - cannot run child processes.')
-        return
-        
     path = os.path.abspath( f'{__file__}/../resources/2.pdf')
     doc = pymupdf.open( path)
     page = doc[5]
@@ -28,14 +24,18 @@ def test_tesseract():
             tail = 'OCR initialisation failed'
         else:
             tail = 'Tesseract language initialisation failed'
-        e_expected = f'code=3: {tail}'
-        if platform.system() == 'OpenBSD':
-            # 2023-12-12: For some reason the SWIG catch code only catches
-            # the exception as FzErrorBase.
-            e_expected_type = pymupdf.mupdf.FzErrorBase
-            print(f'OpenBSD workaround - expecting FzErrorBase, not FzErrorLibrary.')
+        if os.environ.get('PYODIDE_ROOT'):
+            e_expected = 'code=6: No OCR support in this build'
+            e_expected_type = pymupdf.mupdf.FzErrorUnsupported
         else:
-            e_expected_type = pymupdf.mupdf.FzErrorLibrary
+            e_expected = f'code=3: {tail}'
+            if platform.system() == 'OpenBSD':
+                # 2023-12-12: For some reason the SWIG catch code only catches
+                # the exception as FzErrorBase.
+                e_expected_type = pymupdf.mupdf.FzErrorBase
+                print(f'OpenBSD workaround - expecting FzErrorBase, not FzErrorLibrary.')
+            else:
+                e_expected_type = pymupdf.mupdf.FzErrorLibrary
     else:
         # classic.
         e_expected = 'OCR initialisation failed'