diff --git a/backend/swift/swift.go b/backend/swift/swift.go
index 1708db02b..d9de011a3 100644
--- a/backend/swift/swift.go
+++ b/backend/swift/swift.go
@@ -286,6 +286,31 @@ func shouldRetry(err error) (bool, error) {
 	return fserrors.ShouldRetry(err), err
 }
 
+// shouldRetryHeaders returns a boolean as to whether this err
+// deserves to be retried.  It reads the headers passed in looking for
+// `Retry-After`. It returns the err as a convenience
+func shouldRetryHeaders(headers swift.Headers, err error) (bool, error) {
+	if swiftError, ok := err.(*swift.Error); ok && swiftError.StatusCode == 429 {
+		if value := headers["Retry-After"]; value != "" {
+			retryAfter, parseErr := strconv.Atoi(value)
+			if parseErr != nil {
+				fs.Errorf(nil, "Failed to parse Retry-After: %q: %v", value, parseErr)
+			} else {
+				duration := time.Second * time.Duration(retryAfter)
+				if duration <= 60*time.Second {
+					// Do a short sleep immediately
+					fs.Debugf(nil, "Sleeping for %v to obey Retry-After", duration)
+					time.Sleep(duration)
+					return true, err
+				}
+				// Delay a long sleep for a retry
+				return false, fserrors.NewErrorRetryAfter(duration)
+			}
+		}
+	}
+	return shouldRetry(err)
+}
+
 // Pattern to match a swift path
 var matcher = regexp.MustCompile(`^/*([^/]*)(.*)$`)
 
@@ -413,8 +438,9 @@ func NewFsWithConnection(opt *Options, name, root string, c *swift.Connection, n
 		// Check to see if the object exists - ignoring directory markers
 		var info swift.Object
 		err = f.pacer.Call(func() (bool, error) {
-			info, _, err = f.c.Object(container, directory)
-			return shouldRetry(err)
+			var rxHeaders swift.Headers
+			info, rxHeaders, err = f.c.Object(container, directory)
+			return shouldRetryHeaders(rxHeaders, err)
 		})
 		if err == nil && info.ContentType != directoryMarkerContentType {
 			f.root = path.Dir(directory)
@@ -723,8 +749,9 @@ func (f *Fs) Mkdir(dir string) error {
 	var err error = swift.ContainerNotFound
 	if !f.noCheckContainer {
 		err = f.pacer.Call(func() (bool, error) {
-			_, _, err = f.c.Container(f.container)
-			return shouldRetry(err)
+			var rxHeaders swift.Headers
+			_, rxHeaders, err = f.c.Container(f.container)
+			return shouldRetryHeaders(rxHeaders, err)
 		})
 	}
 	if err == swift.ContainerNotFound {
@@ -816,8 +843,9 @@ func (f *Fs) Copy(src fs.Object, remote string) (fs.Object, error) {
 	}
 	srcFs := srcObj.fs
 	err = f.pacer.Call(func() (bool, error) {
-		_, err = f.c.ObjectCopy(srcFs.container, srcFs.root+srcObj.remote, f.container, f.root+remote, nil)
-		return shouldRetry(err)
+		var rxHeaders swift.Headers
+		rxHeaders, err = f.c.ObjectCopy(srcFs.container, srcFs.root+srcObj.remote, f.container, f.root+remote, nil)
+		return shouldRetryHeaders(rxHeaders, err)
 	})
 	if err != nil {
 		return nil, err
@@ -927,7 +955,7 @@ func (o *Object) readMetaData() (err error) {
 	var h swift.Headers
 	err = o.fs.pacer.Call(func() (bool, error) {
 		info, h, err = o.fs.c.Object(o.fs.container, o.fs.root+o.remote)
-		return shouldRetry(err)
+		return shouldRetryHeaders(h, err)
 	})
 	if err != nil {
 		if err == swift.ObjectNotFound {
@@ -1002,8 +1030,9 @@ func (o *Object) Open(options ...fs.OpenOption) (in io.ReadCloser, err error) {
 	headers := fs.OpenOptionHeaders(options)
 	_, isRanging := headers["Range"]
 	err = o.fs.pacer.Call(func() (bool, error) {
-		in, _, err = o.fs.c.ObjectOpen(o.fs.container, o.fs.root+o.remote, !isRanging, headers)
-		return shouldRetry(err)
+		var rxHeaders swift.Headers
+		in, rxHeaders, err = o.fs.c.ObjectOpen(o.fs.container, o.fs.root+o.remote, !isRanging, headers)
+		return shouldRetryHeaders(rxHeaders, err)
 	})
 	return
 }
@@ -1074,8 +1103,9 @@ func (o *Object) updateChunks(in0 io.Reader, headers swift.Headers, size int64,
 	// Create the segmentsContainer if it doesn't exist
 	var err error
 	err = o.fs.pacer.Call(func() (bool, error) {
-		_, _, err = o.fs.c.Container(o.fs.segmentsContainer)
-		return shouldRetry(err)
+		var rxHeaders swift.Headers
+		_, rxHeaders, err = o.fs.c.Container(o.fs.segmentsContainer)
+		return shouldRetryHeaders(rxHeaders, err)
 	})
 	if err == swift.ContainerNotFound {
 		headers := swift.Headers{}
@@ -1115,8 +1145,9 @@ func (o *Object) updateChunks(in0 io.Reader, headers swift.Headers, size int64,
 		segmentPath := fmt.Sprintf("%s/%08d", segmentsPath, i)
 		fs.Debugf(o, "Uploading segment file %q into %q", segmentPath, o.fs.segmentsContainer)
 		err = o.fs.pacer.CallNoRetry(func() (bool, error) {
-			_, err = o.fs.c.ObjectPut(o.fs.segmentsContainer, segmentPath, segmentReader, true, "", "", headers)
-			return shouldRetry(err)
+			var rxHeaders swift.Headers
+			rxHeaders, err = o.fs.c.ObjectPut(o.fs.segmentsContainer, segmentPath, segmentReader, true, "", "", headers)
+			return shouldRetryHeaders(rxHeaders, err)
 		})
 		if err != nil {
 			return "", err
@@ -1129,8 +1160,9 @@ func (o *Object) updateChunks(in0 io.Reader, headers swift.Headers, size int64,
 	emptyReader := bytes.NewReader(nil)
 	manifestName := o.fs.root + o.remote
 	err = o.fs.pacer.Call(func() (bool, error) {
-		_, err = o.fs.c.ObjectPut(o.fs.container, manifestName, emptyReader, true, "", contentType, headers)
-		return shouldRetry(err)
+		var rxHeaders swift.Headers
+		rxHeaders, err = o.fs.c.ObjectPut(o.fs.container, manifestName, emptyReader, true, "", contentType, headers)
+		return shouldRetryHeaders(rxHeaders, err)
 	})
 	return uniquePrefix + "/", err
 }
@@ -1174,7 +1206,7 @@ func (o *Object) Update(in io.Reader, src fs.ObjectInfo, options ...fs.OpenOptio
 		var rxHeaders swift.Headers
 		err = o.fs.pacer.CallNoRetry(func() (bool, error) {
 			rxHeaders, err = o.fs.c.ObjectPut(o.fs.container, o.fs.root+o.remote, in, true, "", contentType, headers)
-			return shouldRetry(err)
+			return shouldRetryHeaders(rxHeaders, err)
 		})
 		if err != nil {
 			return err
diff --git a/backend/swift/swift_internal_test.go b/backend/swift/swift_internal_test.go
index de95a4c67..d9d5b4ca5 100644
--- a/backend/swift/swift_internal_test.go
+++ b/backend/swift/swift_internal_test.go
@@ -1,6 +1,13 @@
 package swift
 
-import "testing"
+import (
+	"testing"
+	"time"
+
+	"github.com/ncw/rclone/fs/fserrors"
+	"github.com/ncw/swift"
+	"github.com/stretchr/testify/assert"
+)
 
 func TestInternalUrlEncode(t *testing.T) {
 	for _, test := range []struct {
@@ -23,3 +30,37 @@ func TestInternalUrlEncode(t *testing.T) {
 		}
 	}
 }
+
+func TestInternalShouldRetryHeaders(t *testing.T) {
+	headers := swift.Headers{
+		"Content-Length": "64",
+		"Content-Type":   "text/html; charset=UTF-8",
+		"Date":           "Mon: 18 Mar 2019 12:11:23 GMT",
+		"Retry-After":    "1",
+	}
+	err := &swift.Error{
+		StatusCode: 429,
+		Text:       "Too Many Requests",
+	}
+
+	// Short sleep should just do the sleep
+	start := time.Now()
+	retry, gotErr := shouldRetryHeaders(headers, err)
+	dt := time.Since(start)
+	assert.True(t, retry)
+	assert.Equal(t, err, gotErr)
+	assert.True(t, dt > time.Second/2)
+
+	// Long sleep should return RetryError
+	headers["Retry-After"] = "3600"
+	start = time.Now()
+	retry, gotErr = shouldRetryHeaders(headers, err)
+	dt = time.Since(start)
+	assert.True(t, dt < time.Second)
+	assert.False(t, retry)
+	assert.Equal(t, true, fserrors.IsRetryAfterError(gotErr))
+	after := gotErr.(fserrors.RetryAfter).RetryAfter()
+	dt = after.Sub(start)
+	assert.True(t, dt >= time.Hour-time.Second && dt <= time.Hour+time.Second)
+
+}