diff --git a/src/calibre/db/cache.py b/src/calibre/db/cache.py
index 3474617e4c..9b98cd79ad 100644
--- a/src/calibre/db/cache.py
+++ b/src/calibre/db/cache.py
@@ -46,7 +46,7 @@ from calibre.ebooks.metadata.book.base import Metadata
 from calibre.ebooks.metadata.opf2 import metadata_to_opf
 from calibre.ptempfile import PersistentTemporaryFile, SpooledTemporaryFile, base_dir
 from calibre.utils.config import prefs, tweaks
-from calibre.utils.date import UNDEFINED_DATE, utcnow
+from calibre.utils.date import UNDEFINED_DATE, timestampfromdt, utcnow
 from calibre.utils.date import now as nowf
 from calibre.utils.filenames import make_long_path_useable
 from calibre.utils.icu import lower as icu_lower
@@ -3158,7 +3158,10 @@ class Cache:
                 mdata = self.format_metadata(book_id, fmt)
                 key = f'{key_prefix}:{book_id}:{fmt}'
                 fm[fmt] = key
-                with exporter.start_file(key, mtime=mdata.get('mtime')) as dest:
+                mtime = mdata.get('mtime')
+                if mtime is not None:
+                    mtime = timestampfromdt(mtime)
+                with exporter.start_file(key, mtime=mtime) as dest:
                     self._copy_format_to(book_id, fmt, dest, report_file_size=dest.ensure_space)
             cover_key = '{}:{}:{}'.format(key_prefix, book_id, '.cover')
             with exporter.start_file(cover_key) as dest:
diff --git a/src/calibre/utils/exim.py b/src/calibre/utils/exim.py
index 21413045cf..b739de617d 100644
--- a/src/calibre/utils/exim.py
+++ b/src/calibre/utils/exim.py
@@ -25,18 +25,6 @@ from polyglot.builtins import error_message, iteritems
 
 # Export {{{
 
-
-def send_file(from_obj, to_obj, chunksize=1<<20):
-    m = hashlib.sha1()
-    while True:
-        raw = from_obj.read(chunksize)
-        if not raw:
-            break
-        m.update(raw)
-        to_obj.write(raw)
-    return str(m.hexdigest())
-
-
 class FileDest:
 
     def __init__(self, key, exporter, mtime=None):
@@ -44,7 +32,7 @@ class FileDest:
         self.hasher = hashlib.sha1()
         self.start_pos = exporter.f.tell()
         self._discard = False
-        self.mtime = None
+        self.mtime = mtime
 
     def discard(self):
         self._discard = True
@@ -59,7 +47,7 @@ class FileDest:
         self.exporter.f.write(data)
 
     def flush(self):
-        pass
+        self.exporter.f.flush()
 
     def close(self):
         if not self._discard:
@@ -127,15 +115,8 @@ class Exporter:
         self.commit_part(is_last=True)
 
     def add_file(self, fileobj, key):
-        fileobj.seek(0, os.SEEK_END)
-        size = fileobj.tell()
-        fileobj.seek(0)
-        self.ensure_space(size)
-        pos = self.f.tell()
-        digest = send_file(fileobj, self.f)
-        size = self.f.tell() - pos
-        mtime = os.fstat(fileobj.fileno()).st_mtime
-        self.file_metadata[key] = (len(self.parts), pos, size, digest, mtime)
+        with self.start_file(key, os.fstat(fileobj.fileno()).st_mtime) as dest:
+            shutil.copyfileobj(fileobj, dest)
 
     def start_file(self, key, mtime=None):
         return FileDest(key, self, mtime=mtime)