diff --git a/tests/avocado/machine_m68k_nextcube.py b/tests/avocado/machine_m68k_nextcube.py
index f1205d7fc0..1f3c883910 100644
--- a/tests/avocado/machine_m68k_nextcube.py
+++ b/tests/avocado/machine_m68k_nextcube.py
@@ -55,25 +55,16 @@ class NextCubeMachine(QemuSystemTest):
         self.assertEqual(width, 1120)
         self.assertEqual(height, 832)
 
-    @skipUnless(tesseract_available(3), 'tesseract v3 OCR tool not available')
-    def test_bootrom_framebuffer_ocr_with_tesseract_v3(self):
-        screenshot_path = os.path.join(self.workdir, "dump.ppm")
-        self.check_bootrom_framebuffer(screenshot_path)
-        lines = tesseract_ocr(screenshot_path, tesseract_version=3)
-        text = '\n'.join(lines)
-        self.assertIn('Backplane', text)
-        self.assertIn('Ethernet address', text)
-
     # Tesseract 4 adds a new OCR engine based on LSTM neural networks. The
     # new version is faster and more accurate than version 3. The drawback is
     # that it is still alpha-level software.
-    @skipUnless(tesseract_available(4), 'tesseract v4 OCR tool not available')
-    def test_bootrom_framebuffer_ocr_with_tesseract_v4(self):
+    @skipUnless(tesseract_available(4), 'tesseract OCR tool not available')
+    def test_bootrom_framebuffer_ocr_with_tesseract(self):
         screenshot_path = os.path.join(self.workdir, "dump.ppm")
         self.check_bootrom_framebuffer(screenshot_path)
         lines = tesseract_ocr(screenshot_path, tesseract_version=4)
         text = '\n'.join(lines)
-        self.assertIn('Testing the FPU, SCC', text)
+        self.assertIn('Testing the FPU', text)
         self.assertIn('System test failed. Error code', text)
         self.assertIn('Boot command', text)
         self.assertIn('Next>', text)
diff --git a/tests/avocado/tesseract_utils.py b/tests/avocado/tesseract_utils.py
index 72cd9ab798..476f528147 100644
--- a/tests/avocado/tesseract_utils.py
+++ b/tests/avocado/tesseract_utils.py
@@ -21,13 +21,13 @@ def tesseract_available(expected_version):
         version = res.stdout_text.split()[1]
     except IndexError:
         version = res.stderr_text.split()[1]
-    return int(version.split('.')[0]) == expected_version
+    return int(version.split('.')[0]) >= expected_version
 
     match = re.match(r'tesseract\s(\d)', res)
     if match is None:
         return False
     # now this is guaranteed to be a digit
-    return int(match.groups()[0]) == expected_version
+    return int(match.groups()[0]) >= expected_version
 
 
 def tesseract_ocr(image_path, tesseract_args='', tesseract_version=3):