diff --git a/CHANGELOG b/CHANGELOG
index d6420e03a2..0a492f966c 100644
--- a/CHANGELOG
+++ b/CHANGELOG
@@ -4,6 +4,7 @@ git-annex (8.20200523) UNRELEASED; urgency=medium
   * import: Added --json-progress.
   * addurl: Make --preserve-filename also apply when eg a torrent contains
     multiple files.
+  * export: Let concurrent transfers be done with -J or annex.jobs.
 
  -- Joey Hess <id@joeyh.name>  Tue, 26 May 2020 10:20:52 -0400
 
diff --git a/Command/Export.hs b/Command/Export.hs
index 187f5f2163..82f3b8d962 100644
--- a/Command/Export.hs
+++ b/Command/Export.hs
@@ -44,7 +44,7 @@ import qualified Data.Map as M
 import Control.Concurrent
 
 cmd :: Command
-cmd = withGlobalOptions [jsonOptions, jsonProgressOption] $
+cmd = withGlobalOptions [jobsOption, jsonOptions, jsonProgressOption] $
 	command "export" SectionCommon
 		"export content to a remote"
 		paramTreeish (seek <$$> optParser)
@@ -77,7 +77,7 @@ exportTempName ek = mkExportLocation $ toRawFilePath $
 	".git-annex-tmp-content-" ++ serializeKey (asKey (ek))
 
 seek :: ExportOptions -> CommandSeek
-seek o = do
+seek o = startConcurrency commandStages $ do
 	r <- getParsed (exportRemote o)
 	unlessM (isExportSupported r) $
 		giveup "That remote does not support exports."
diff --git a/doc/bugs/sync_to_export_with-J_STM_error.mdwn b/doc/bugs/sync_to_export_with-J_STM_error.mdwn
new file mode 100644
index 0000000000..a0cb177821
--- /dev/null
+++ b/doc/bugs/sync_to_export_with-J_STM_error.mdwn
@@ -0,0 +1,13 @@
+git annex sync exportremote -J2 --content
+
+git-annex: thread blocked indefinitely in an MVar operation
+failed
+git-annex: thread blocked indefinitely in an STM transaction
+
+Also, git-annex export -J2 crashes the same way. I discovered this bug
+when adding -J to export, but then found sync had the same bug.
+
+To reproduce this, there may need there to be a tree of several annexed 
+files whose content is not locally available. In my case,
+there were 338 of them. It seems to export all, or all but 1
+before crashing. --[[Joey]]
diff --git a/doc/git-annex-export.mdwn b/doc/git-annex-export.mdwn
index b081a26fca..0445ee5a71 100644
--- a/doc/git-annex-export.mdwn
+++ b/doc/git-annex-export.mdwn
@@ -86,6 +86,13 @@ so the overwritten modification is not lost.)
   the remote. You can later run `git annex sync --content` to upload
   the files to the export.
 
+* `--jobs=N` `-JN`
+
+  Exports multiple files in parallel. This may be faster.
+  For example: `-J4`  
+
+  Setting this to "cpus" will run one job per CPU core.
+
 * `--json`
 
   Enable JSON output. This is intended to be parsed by programs that use