diff --git a/hail/python/hailtop/aiotools/fs/copier.py b/hail/python/hailtop/aiotools/fs/copier.py
index b367c069e48..913f00da4a6 100644
--- a/hail/python/hailtop/aiotools/fs/copier.py
+++ b/hail/python/hailtop/aiotools/fs/copier.py
@@ -1,4 +1,4 @@
-from typing import Any, AsyncIterator, Awaitable, Optional, List, Union, Dict, Callable
+from typing import Any, AsyncIterator, Awaitable, Optional, List, Union, Dict, Callable, Tuple
 import os
 import os.path
 import asyncio
@@ -163,7 +163,10 @@ def add_source_reports(transfer_report):
         print(f'  Time: {humanize_timedelta_msecs(self._duration)}')
         assert self._duration is not None
         if self._duration > 0:
-            print(f'  Average transfer rate: {humanize.naturalsize(total_bytes / (self._duration / 1000))}/s')
+            bandwidth = humanize.naturalsize(total_bytes / (self._duration / 1000))
+            print(f'  Average bandwidth: {bandwidth}/s')
+            file_rate = total_files / (self._duration / 1000)
+            print(f'  Average file rate: {file_rate:,.1f}/s')
 
         print('Sources:')
         for sr in source_reports:
@@ -289,8 +292,6 @@ async def _copy_file_multi_part(
             destfile: str,
             return_exceptions: bool
     ) -> None:
-        source_report.start_files(1)
-        source_report.start_bytes(await srcstat.size())
         success = False
         try:
             await self._copy_file_multi_part_main(sema, source_report, srcfile, srcstat, destfile, return_exceptions)
@@ -350,6 +351,8 @@ async def copy_as_file(self,
         if full_dest_type == AsyncFS.DIR:
             raise IsADirectoryError(full_dest)
 
+        source_report.start_files(1)
+        source_report.start_bytes(await srcstat.size())
         await self._copy_file_multi_part(sema, source_report, src, srcstat, full_dest, return_exceptions)
 
     async def copy_as_dir(self, sema: asyncio.Semaphore, source_report: SourceReport, return_exceptions: bool):
@@ -394,19 +397,26 @@ async def copy_source(srcentry: FileListEntry) -> None:
 
             await self._copy_file_multi_part(sema, source_report, srcfile, await srcentry.status(), url_join(full_dest, relsrcfile), return_exceptions)
 
-        async def create_copies() -> List[Callable[[], Awaitable[None]]]:
+        async def create_copies() -> Tuple[List[Callable[[], Awaitable[None]]], int]:
             nonlocal srcentries
+            bytes_to_copy = 0
             if srcentries is None:
                 srcentries = await files_iterator()
             try:
-                return [
-                    functools.partial(copy_source, srcentry)
-                    async for srcentry in srcentries]
+                copy_thunks = []
+                async for srcentry in srcentries:
+                    # In cloud FSes, status and size never make a network request. In local FS, they
+                    # can make system calls on symlinks. This line will be fairly expensive if
+                    # copying a tree with a lot of symlinks.
+                    bytes_to_copy += await (await srcentry.status()).size()
+                    copy_thunks.append(functools.partial(copy_source, srcentry))
+                return (copy_thunks, bytes_to_copy)
             finally:
                 srcentries = None
 
-        copies = await retry_transient_errors(create_copies)
-
+        copies, bytes_to_copy = await retry_transient_errors(create_copies)
+        source_report.start_files(len(copies))
+        source_report.start_bytes(bytes_to_copy)
         await bounded_gather2(sema, *copies, cancel_on_error=True)
 
     async def copy(self, sema: asyncio.Semaphore, source_report: SourceReport, return_exceptions: bool):