diff --git a/fs/chunkedreader/chunkedreader.go b/fs/chunkedreader/chunkedreader.go
index fb135b83d..4a4a62cf3 100644
--- a/fs/chunkedreader/chunkedreader.go
+++ b/fs/chunkedreader/chunkedreader.go
@@ -1,43 +1,55 @@
 package chunkedreader
 
 import (
+	"errors"
 	"io"
 	"sync"
 
 	"github.com/ncw/rclone/fs"
 )
 
+// io related errors returned by ChunkedReader
+var (
+	ErrorFileClosed  = errors.New("file already closed")
+	ErrorInvalidSeek = errors.New("invalid seek position")
+)
+
 // ChunkedReader is a reader for a Object with the possibility
 // of reading the source in chunks of given size
 //
-// A initialChunkSize of 0 will disable chunked reading.
+// A initialChunkSize of <= 0 will disable chunked reading.
 type ChunkedReader struct {
-	mu               sync.Mutex
-	o                fs.Object
-	rc               io.ReadCloser
-	offset           int64
-	chunkOffset      int64
-	chunkSize        int64
-	initialChunkSize int64
-	chunkGrowth      bool
-	doSeek           bool
+	mu               sync.Mutex    // protects following fields
+	o                fs.Object     // source to read from
+	rc               io.ReadCloser // reader for the current open chunk
+	offset           int64         // offset the next Read will start. -1 forces a reopen of o
+	chunkOffset      int64         // beginning of the current or next chunk
+	chunkSize        int64         // length of the current or next chunk. -1 will open o from chunkOffset to the end
+	initialChunkSize int64         // default chunkSize after the chunk specified by RangeSeek is complete
+	maxChunkSize     int64         // consecutive read chunks will double in size until reached. -1 means no limit
+	customChunkSize  bool          // is the current chunkSize set by RangeSeek?
+	closed           bool          // has Close been called?
 }
 
 // New returns a ChunkedReader for the Object.
 //
-// A initialChunkSize of 0 will disable chunked reading.
-// If chunkGrowth is true, the chunk size will be doubled after each chunk read.
+// A initialChunkSize of <= 0 will disable chunked reading.
+// If maxChunkSize is greater than initialChunkSize, the chunk size will be
+// doubled after each chunk read with a maximun of maxChunkSize.
 // A Seek or RangeSeek will reset the chunk size to it's initial value
-func New(o fs.Object, initialChunkSize int64, chunkGrowth bool) *ChunkedReader {
-	if initialChunkSize < 0 {
-		initialChunkSize = 0
+func New(o fs.Object, initialChunkSize int64, maxChunkSize int64) *ChunkedReader {
+	if initialChunkSize <= 0 {
+		initialChunkSize = -1
+	}
+	if maxChunkSize != -1 && maxChunkSize < initialChunkSize {
+		maxChunkSize = initialChunkSize
 	}
 	return &ChunkedReader{
 		o:                o,
 		offset:           -1,
 		chunkSize:        initialChunkSize,
 		initialChunkSize: initialChunkSize,
-		chunkGrowth:      chunkGrowth,
+		maxChunkSize:     maxChunkSize,
 	}
 }
 
@@ -46,21 +58,32 @@ func (cr *ChunkedReader) Read(p []byte) (n int, err error) {
 	cr.mu.Lock()
 	defer cr.mu.Unlock()
 
+	if cr.closed {
+		return 0, ErrorFileClosed
+	}
+
 	for reqSize := int64(len(p)); reqSize > 0; reqSize = int64(len(p)) {
+		// the current chunk boundary. valid only when chunkSize > 0
 		chunkEnd := cr.chunkOffset + cr.chunkSize
 
 		fs.Debugf(cr.o, "ChunkedReader.Read at %d length %d chunkOffset %d chunkSize %d", cr.offset, reqSize, cr.chunkOffset, cr.chunkSize)
 
-		if atChunkEnd := cr.offset == chunkEnd; cr.offset == -1 || atChunkEnd {
-			if atChunkEnd && cr.chunkSize > 0 {
-				if cr.doSeek {
-					cr.doSeek = false
-					cr.chunkSize = cr.initialChunkSize
-				} else if cr.chunkGrowth {
-					cr.chunkSize *= 2
+		switch {
+		case cr.chunkSize > 0 && cr.offset == chunkEnd: // last chunk read completely
+			cr.chunkOffset = cr.offset
+			if cr.customChunkSize { // last chunkSize was set by RangeSeek
+				cr.customChunkSize = false
+				cr.chunkSize = cr.initialChunkSize
+			} else {
+				cr.chunkSize *= 2
+				if cr.chunkSize > cr.maxChunkSize && cr.maxChunkSize != -1 {
+					cr.chunkSize = cr.maxChunkSize
 				}
-				cr.chunkOffset = cr.offset
 			}
+			// recalculate the chunk boundary. valid only when chunkSize > 0
+			chunkEnd = cr.chunkOffset + cr.chunkSize
+			fallthrough
+		case cr.offset == -1: // first Read or Read after RangeSeek
 			err = cr.openRange()
 			if err != nil {
 				return
@@ -69,7 +92,8 @@ func (cr *ChunkedReader) Read(p []byte) (n int, err error) {
 
 		var buf []byte
 		chunkRest := chunkEnd - cr.offset
-		if reqSize > chunkRest && cr.chunkSize != 0 {
+		// limit read to chunk boundaries if chunkSize > 0
+		if reqSize > chunkRest && cr.chunkSize > 0 {
 			buf, p = p[0:chunkRest], p[chunkRest:]
 		} else {
 			buf, p = p, nil
@@ -79,6 +103,9 @@ func (cr *ChunkedReader) Read(p []byte) (n int, err error) {
 		n += rn
 		cr.offset += int64(rn)
 		if err != nil {
+			if err == io.ErrUnexpectedEOF {
+				err = io.EOF
+			}
 			return
 		}
 	}
@@ -86,10 +113,17 @@ func (cr *ChunkedReader) Read(p []byte) (n int, err error) {
 }
 
 // Close the file - for details see io.Closer
+//
+// All methods on ChunkedReader will return ErrorFileClosed afterwards
 func (cr *ChunkedReader) Close() error {
 	cr.mu.Lock()
 	defer cr.mu.Unlock()
 
+	if cr.closed {
+		return ErrorFileClosed
+	}
+	cr.closed = true
+
 	return cr.resetReader(nil, 0)
 }
 
@@ -99,11 +133,18 @@ func (cr *ChunkedReader) Seek(offset int64, whence int) (int64, error) {
 }
 
 // RangeSeek the file - for details see RangeSeeker
+//
+// The specified length will only apply to the next chunk opened.
+// RangeSeek will not reopen the source until Read is called.
 func (cr *ChunkedReader) RangeSeek(offset int64, whence int, length int64) (int64, error) {
 	cr.mu.Lock()
 	defer cr.mu.Unlock()
 
-	fs.Debugf(cr.o, "ChunkedReader.RangeSeek from %d to %d", cr.offset, offset)
+	fs.Debugf(cr.o, "ChunkedReader.RangeSeek from %d to %d length %d", cr.offset, offset, length)
+
+	if cr.closed {
+		return 0, ErrorFileClosed
+	}
 
 	size := cr.o.Size()
 	switch whence {
@@ -112,15 +153,21 @@ func (cr *ChunkedReader) RangeSeek(offset int64, whence int, length int64) (int6
 	case io.SeekEnd:
 		cr.offset = size
 	}
+	// set the new chunk start
 	cr.chunkOffset = cr.offset + offset
+	// force reopen on next Read
 	cr.offset = -1
-	cr.doSeek = true
 	if length > 0 {
+		cr.customChunkSize = true
 		cr.chunkSize = length
 	} else {
 		cr.chunkSize = cr.initialChunkSize
 	}
-	return cr.offset, nil
+	if cr.chunkOffset < 0 || cr.chunkOffset >= size {
+		cr.chunkOffset = 0
+		return 0, ErrorInvalidSeek
+	}
+	return cr.chunkOffset, nil
 }
 
 // Open forces the connection to be opened
@@ -128,15 +175,39 @@ func (cr *ChunkedReader) Open() (*ChunkedReader, error) {
 	cr.mu.Lock()
 	defer cr.mu.Unlock()
 
+	if cr.rc != nil && cr.offset != -1 {
+		return cr, nil
+	}
 	return cr, cr.openRange()
 }
 
-// openRange will open the source Object with the given range
+// openRange will open the source Object with the current chunk range
+//
+// If the current open reader implenets RangeSeeker, it is tried first.
+// When RangeSeek failes, o.Open with a RangeOption is used.
+//
 // A length <= 0 will request till the end of the file
 func (cr *ChunkedReader) openRange() error {
 	offset, length := cr.chunkOffset, cr.chunkSize
 	fs.Debugf(cr.o, "ChunkedReader.openRange at %d length %d", offset, length)
 
+	if cr.closed {
+		return ErrorFileClosed
+	}
+
+	if rs, ok := cr.rc.(fs.RangeSeeker); ok {
+		n, err := rs.RangeSeek(offset, io.SeekStart, length)
+		if err == nil && n == offset {
+			cr.offset = offset
+			return nil
+		}
+		if err != nil {
+			fs.Debugf(cr.o, "ChunkedReader.openRange seek failed (%s). Trying Open", err)
+		} else {
+			fs.Debugf(cr.o, "ChunkedReader.openRange seeked to wrong offset. Wanted %d, got %d. Trying Open", offset, n)
+		}
+	}
+
 	var rc io.ReadCloser
 	var err error
 	if length <= 0 {
diff --git a/fs/chunkedreader/chunkedreader_test.go b/fs/chunkedreader/chunkedreader_test.go
new file mode 100644
index 000000000..71a0a449e
--- /dev/null
+++ b/fs/chunkedreader/chunkedreader_test.go
@@ -0,0 +1,111 @@
+package chunkedreader
+
+import (
+	"fmt"
+	"io"
+	"math/rand"
+	"testing"
+
+	"github.com/ncw/rclone/fstest/mockobject"
+	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
+)
+
+func TestChunkedReader(t *testing.T) {
+	content := makeContent(t, 1024)
+
+	for _, mode := range mockobject.SeekModes {
+		t.Run(mode.String(), testRead(content, mode))
+	}
+}
+
+func testRead(content []byte, mode mockobject.SeekMode) func(*testing.T) {
+	return func(t *testing.T) {
+		chunkSizes := []int64{-1, 0, 1, 15, 16, 17, 1023, 1024, 1025, 2000}
+		offsets := []int64{0, 1, 2, 3, 4, 5, 7, 8, 9, 15, 16, 17, 31, 32, 33,
+			63, 64, 65, 511, 512, 513, 1023, 1024, 1025}
+		limits := []int64{-1, 0, 1, 31, 32, 33, 1023, 1024, 1025}
+		cl := int64(len(content))
+		bl := 32
+		buf := make([]byte, bl)
+
+		o := mockobject.New("test.bin").WithContent(content, mode)
+		for ics, cs := range chunkSizes {
+			for icsMax, csMax := range chunkSizes {
+				// skip tests where chunkSize is much bigger than maxChunkSize
+				if ics > icsMax+1 {
+					continue
+				}
+
+				t.Run(fmt.Sprintf("Chunksize_%d_%d", cs, csMax), func(t *testing.T) {
+					cr := New(o, cs, csMax)
+
+					for _, offset := range offsets {
+						for _, limit := range limits {
+							what := fmt.Sprintf("offset %d, limit %d", offset, limit)
+
+							p, err := cr.RangeSeek(offset, io.SeekStart, limit)
+							if offset >= cl {
+								require.Error(t, err, what)
+								return
+							}
+							require.NoError(t, err, what)
+							require.Equal(t, offset, p, what)
+
+							n, err := cr.Read(buf)
+							end := offset + int64(bl)
+							if end > cl {
+								end = cl
+							}
+							l := int(end - offset)
+							if l < bl {
+								require.Equal(t, io.EOF, err, what)
+							} else {
+								require.NoError(t, err, what)
+							}
+							require.Equal(t, l, n, what)
+							require.Equal(t, content[offset:end], buf[:n], what)
+						}
+					}
+				})
+			}
+		}
+	}
+}
+
+func TestErrorAfterClose(t *testing.T) {
+	content := makeContent(t, 1024)
+	o := mockobject.New("test.bin").WithContent(content, mockobject.SeekModeNone)
+
+	// Close
+	cr := New(o, 0, 0)
+	require.NoError(t, cr.Close())
+	require.Error(t, cr.Close())
+
+	// Read
+	cr = New(o, 0, 0)
+	require.NoError(t, cr.Close())
+	var buf [1]byte
+	_, err := cr.Read(buf[:])
+	require.Error(t, err)
+
+	// Seek
+	cr = New(o, 0, 0)
+	require.NoError(t, cr.Close())
+	_, err = cr.Seek(1, io.SeekCurrent)
+	require.Error(t, err)
+
+	// RangeSeek
+	cr = New(o, 0, 0)
+	require.NoError(t, cr.Close())
+	_, err = cr.RangeSeek(1, io.SeekCurrent, 0)
+	require.Error(t, err)
+}
+
+func makeContent(t *testing.T, size int) []byte {
+	content := make([]byte, size)
+	r := rand.New(rand.NewSource(42))
+	_, err := io.ReadFull(r, content)
+	assert.NoError(t, err)
+	return content
+}
diff --git a/fstest/mockobject/mockobject.go b/fstest/mockobject/mockobject.go
index 9c83987a3..afeaad8ab 100644
--- a/fstest/mockobject/mockobject.go
+++ b/fstest/mockobject/mockobject.go
@@ -2,7 +2,9 @@
 package mockobject
 
 import (
+	"bytes"
 	"errors"
+	"fmt"
 	"io"
 	"time"
 
@@ -15,6 +17,11 @@ var errNotImpl = errors.New("not implemented")
 // Object is a mock fs.Object useful for testing
 type Object string
 
+// New returns mock fs.Object useful for testing
+func New(name string) Object {
+	return Object(name)
+}
+
 // String returns a description of the Object
 func (o Object) String() string {
 	return string(o)
@@ -69,3 +76,105 @@ func (o Object) Update(in io.Reader, src fs.ObjectInfo, options ...fs.OpenOption
 func (o Object) Remove() error {
 	return errNotImpl
 }
+
+// SeekMode specifies the optional Seek interface for the ReadCloser returned by Open
+type SeekMode int
+
+const (
+	// SeekModeNone specifies no seek interface
+	SeekModeNone SeekMode = iota
+	// SeekModeRegular specifies the regular io.Seek interface
+	SeekModeRegular
+	// SeekModeRange specifies the fs.RangeSeek interface
+	SeekModeRange
+)
+
+// SeekModes contains all valid SeekMode's
+var SeekModes = []SeekMode{SeekModeNone, SeekModeRegular, SeekModeRange}
+
+type contentMockObject struct {
+	Object
+	content  []byte
+	seekMode SeekMode
+}
+
+// WithContent returns a fs.Object with the given content.
+func (o Object) WithContent(content []byte, mode SeekMode) fs.Object {
+	return &contentMockObject{
+		Object:   o,
+		content:  content,
+		seekMode: mode,
+	}
+}
+
+func (o *contentMockObject) Open(options ...fs.OpenOption) (io.ReadCloser, error) {
+	var offset, limit int64 = 0, -1
+	for _, option := range options {
+		switch x := option.(type) {
+		case *fs.SeekOption:
+			offset = x.Offset
+		case *fs.RangeOption:
+			offset, limit = x.Decode(o.Size())
+		default:
+			if option.Mandatory() {
+				return nil, fmt.Errorf("Unsupported mandatory option: %v", option)
+			}
+		}
+	}
+	if limit == -1 || offset+limit > o.Size() {
+		limit = o.Size() - offset
+	}
+
+	var r *bytes.Reader
+	if o.seekMode == SeekModeNone {
+		r = bytes.NewReader(o.content[offset : offset+limit])
+	} else {
+		r = bytes.NewReader(o.content)
+		_, err := r.Seek(offset, io.SeekStart)
+		if err != nil {
+			return nil, err
+		}
+	}
+	switch o.seekMode {
+	case SeekModeNone:
+		return &readCloser{r}, nil
+	case SeekModeRegular:
+		return &readSeekCloser{r}, nil
+	case SeekModeRange:
+		return &readRangeSeekCloser{r}, nil
+	default:
+		return nil, errors.New(o.seekMode.String())
+	}
+}
+func (o *contentMockObject) Size() int64 {
+	return int64(len(o.content))
+}
+
+type readCloser struct{ io.Reader }
+
+func (r *readCloser) Close() error { return nil }
+
+type readSeekCloser struct{ io.ReadSeeker }
+
+func (r *readSeekCloser) Close() error { return nil }
+
+type readRangeSeekCloser struct{ io.ReadSeeker }
+
+func (r *readRangeSeekCloser) RangeSeek(offset int64, whence int, length int64) (int64, error) {
+	return r.ReadSeeker.Seek(offset, whence)
+}
+
+func (r *readRangeSeekCloser) Close() error { return nil }
+
+func (m SeekMode) String() string {
+	switch m {
+	case SeekModeNone:
+		return "SeekModeNone"
+	case SeekModeRegular:
+		return "SeekModeRegular"
+	case SeekModeRange:
+		return "SeekModeRange"
+	default:
+		return fmt.Sprintf("SeekModeInvalid(%d)", m)
+	}
+}