@@ -280,8 +280,9 @@ def get_readable_fileobj(name_or_obj, encoding=None, cache=False,
         except ImportError:
             for fd in close_fds:
                 fd.close()
-            raise ModuleNotFoundError(
-                "This Python installation does not provide the bz2 module.")
+            raise ValueError(
+                ".bz2 format files are not supported since the Python "
+                "interpreter does not include the bz2 module")
         try:
             # bz2.BZ2File does not support file objects, only filenames, so we
             # need to write the data to a temporary file
@@ -306,8 +307,9 @@ def get_readable_fileobj(name_or_obj, encoding=None, cache=False,
         except ImportError:
             for fd in close_fds:
                 fd.close()
-            raise ModuleNotFoundError(
-                "This Python installation does not provide the lzma module.")
+            raise ValueError(
+                ".xz format files are not supported since the Python "
+                "interpreter does not include the lzma module.")
         except (OSError, EOFError):  # invalid xz file
             fileobj.seek(0)
             fileobj_new.close()
 
@@ -168,8 +168,7 @@ Working with compressed files
 The :func:`open` function will seamlessly open FITS files that have been
 compressed with gzip, bzip2 or pkzip. Note that in this context we are talking
 about a FITS file that has been compressed with one of these utilities (e.g., a
-.fits.gz file). Opening bzip2-compressed files requires the :mod:`bz2` module
-to be available.
+.fits.gz file).
 
 There are some limitations when working with compressed files. For example,
 with Zip files that contain multiple compressed files, only the first file will