diff --git a/grayskull/license/discovery.py b/grayskull/license/discovery.py
index 9fa74f929..3bac764e5 100644
--- a/grayskull/license/discovery.py
+++ b/grayskull/license/discovery.py
@@ -82,7 +82,20 @@ def match_license(name: str) -> dict:
     spdx_license = best_matches[0]
 
     if spdx_license[1] < 100:
-        best_matches = [lic[0] for lic in best_matches if not lic[0].endswith("-only")]
+        # Prefer "-or-later" licenses over the "-only"
+        later_licenses = {
+            lic[0].replace("-or-later", "")
+            for lic in best_matches
+            if lic[0].endswith("-or-later")
+        }
+        best_matches = [
+            lic[0]
+            for lic in best_matches
+            if not (
+                lic[0].endswith("-only")
+                and lic[0].replace("-only", "") in later_licenses
+            )
+        ]
 
         if best_matches:
             best_matches = process.extract(
@@ -102,7 +115,7 @@ def match_license(name: str) -> dict:
                 spdx_license = process.extractOne(
                     name, best_matches, scorer=token_sort_ratio
                 )
-            if original_matches[0][1] < 0.55:
+            if original_matches and original_matches[0][1] < 0.55:
                 spdx_license = process.extractOne(
                     name, [m[0] for m in original_matches], scorer=token_sort_ratio
                 )
diff --git a/tests/license/test_discovery.py b/tests/license/test_discovery.py
index 8840ee8da..6bb8dff76 100644
--- a/tests/license/test_discovery.py
+++ b/tests/license/test_discovery.py
@@ -64,7 +64,11 @@ def test_get_opensource_license_data():
         ("MIT License", "MIT"),
         ("Expat", "MIT"),
         ("GPL 2.0", "GPL-2.0-or-later"),
-        ("GPLv3", "GPL-3.0-or-later"),
+        ("GPL 3.0", "GPL-3.0-only"),
+        ("GPLv3", "GPL-3.0-only"),
+        ("GPL-3.0-only", "GPL-3.0-only"),
+        ("LGPL 2.0", "LGPL-2.0-or-later"),
+        ("LGPL-3.0-or-later", "LGPL-3.0-or-later"),
         ("2-Clause BSD License", "BSD-2-Clause"),
         ("3-Clause BSD License", "BSD-3-Clause"),
     ],