diff --git a/attic/archive.py b/attic/archive.py
index f42c477a9..208e8cb98 100644
--- a/attic/archive.py
+++ b/attic/archive.py
@@ -613,7 +613,9 @@ class ArchiveChecker:
                 continue
             try:
                 archive = msgpack.unpackb(data)
-            except Exception:
+            # Ignore exceptions that might be raised when feeding
+            # msgpack with invalid data
+            except (TypeError, ValueError, StopIteration):
                 continue
             if isinstance(archive, dict) and b'items' in archive and b'cmdline' in archive:
                 self.report_progress('Found archive ' + archive[b'name'].decode('utf-8'), error=True)
diff --git a/attic/repository.py b/attic/repository.py
index b5f11d7a7..255382f61 100644
--- a/attic/repository.py
+++ b/attic/repository.py
@@ -446,7 +446,7 @@ class LoggedIO:
         with open(filename, 'rb') as fd:
             try:
                 fd.seek(-self.header_fmt.size, os.SEEK_END)
-            except Exception as e:
+            except OSError as e:
                 # return False if segment file is empty or too small
                 if e.errno == errno.EINVAL:
                     return False