diff --git a/go.mod b/go.mod
index 81d35692f..a2c301d15 100644
--- a/go.mod
+++ b/go.mod
@@ -38,7 +38,7 @@ require (
 	golang.org/x/crypto v0.0.0-20220321153916-2c7772ba3064
 	golang.org/x/net v0.0.0-20220325170049-de3da57026de
 	golang.org/x/oauth2 v0.0.0-20220309155454-6242fa91716a
-	golang.org/x/sync v0.0.0-20210220032951-036812b2e83c
+	golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4
 	golang.org/x/sys v0.0.0-20220325203850-36772127a21f
 	golang.org/x/term v0.0.0-20210927222741-03fcf44c2211
 	golang.org/x/text v0.3.7
diff --git a/go.sum b/go.sum
index 4f1ff9309..54711322a 100644
--- a/go.sum
+++ b/go.sum
@@ -439,8 +439,9 @@ golang.org/x/sync v0.0.0-20200317015054-43a5402ce75a/go.mod h1:RxMgew5VJxzue5/jJ
 golang.org/x/sync v0.0.0-20200625203802-6e8e738ad208/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sync v0.0.0-20201020160332-67f06af15bc9/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sync v0.0.0-20201207232520-09787c993a3a/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
-golang.org/x/sync v0.0.0-20210220032951-036812b2e83c h1:5KslGYwFpkhGh+Q16bwMP3cOontH8FOep7tGV86Y7SQ=
 golang.org/x/sync v0.0.0-20210220032951-036812b2e83c/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
+golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4 h1:uVc8UZUe6tr40fFVnUP5Oj+veunVezqYl9z7DYw9xzw=
+golang.org/x/sync v0.0.0-20220722155255-886fb9371eb4/go.mod h1:RxMgew5VJxzue5/jJTE5uejpjVlOe/izrB70Jof72aM=
 golang.org/x/sys v0.0.0-20180830151530-49385e6e1522/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
 golang.org/x/sys v0.0.0-20190215142949-d0b11bdaac8a/go.mod h1:STP8DvDyc/dI5b8T5hshtkjS+E42TnysNCUPdjciGhY=
 golang.org/x/sys v0.0.0-20190312061237-fead79001313/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=
diff --git a/internal/backend/sftp/sftp.go b/internal/backend/sftp/sftp.go
index e0edb807c..0aa2700a6 100644
--- a/internal/backend/sftp/sftp.go
+++ b/internal/backend/sftp/sftp.go
@@ -21,6 +21,7 @@ import (
 
 	"github.com/cenkalti/backoff/v4"
 	"github.com/pkg/sftp"
+	"golang.org/x/sync/errgroup"
 )
 
 // SFTP is a backend in a directory accessed via SFTP.
@@ -154,15 +155,29 @@ func Open(ctx context.Context, cfg Config) (*SFTP, error) {
 	return sftp, nil
 }
 
-func (r *SFTP) mkdirAllDataSubdirs() error {
+func (r *SFTP) mkdirAllDataSubdirs(ctx context.Context, nconn uint) error {
+	// Run multiple MkdirAll calls concurrently. These involve multiple
+	// round-trips and we do a lot of them, so this whole operation can be slow
+	// on high-latency links.
+	g, _ := errgroup.WithContext(ctx)
+	// Use errgroup's built-in semaphore, because r.sem is not initialized yet.
+	g.SetLimit(int(nconn))
+
 	for _, d := range r.Paths() {
-		err := r.c.MkdirAll(d)
-		if err != nil {
-			return err
-		}
+		d := d
+		g.Go(func() error {
+			// First try Mkdir. For most directories in Paths, this takes one
+			// round trip, not counting duplicate parent creations causes by
+			// concurrency. MkdirAll first does Stat, then recursive MkdirAll
+			// on the parent, so calls typically take three round trips.
+			if err := r.c.Mkdir(d); err == nil {
+				return nil
+			}
+			return r.c.MkdirAll(d)
+		})
 	}
 
-	return nil
+	return g.Wait()
 }
 
 // Join combines path components with slashes (according to the sftp spec).
@@ -240,7 +255,7 @@ func Create(ctx context.Context, cfg Config) (*SFTP, error) {
 	}
 
 	// create paths for data and refs
-	if err = sftp.mkdirAllDataSubdirs(); err != nil {
+	if err = sftp.mkdirAllDataSubdirs(ctx, cfg.Connections); err != nil {
 		return nil, err
 	}