diff --git a/beets/importer.py b/beets/importer.py
index e97b0a75c..68d5f3d5d 100644
--- a/beets/importer.py
+++ b/beets/importer.py
@@ -1034,8 +1034,8 @@ class ArchiveImportTask(SentinelImportTask):
             cls._handlers = []
             from zipfile import is_zipfile, ZipFile
             cls._handlers.append((is_zipfile, ZipFile))
-            from tarfile import is_tarfile, TarFile
-            cls._handlers.append((is_tarfile, TarFile))
+            import tarfile
+            cls._handlers.append((tarfile.is_tarfile, tarfile.open))
             try:
                 from rarfile import is_rarfile, RarFile
             except ImportError:
diff --git a/docs/changelog.rst b/docs/changelog.rst
index 3f2890913..21cbd1217 100644
--- a/docs/changelog.rst
+++ b/docs/changelog.rst
@@ -124,6 +124,8 @@ New features:
   separators to support path queries.
   Thanks to :user:`nmeum`.
   :bug:`3567`
+* ``beet import`` now handles tar archives with bzip2 or gzip compression.
+  :bug:`3606`
 
 Fixes: