diff --git a/fs/operations/check.go b/fs/operations/check.go
index f96efb139..06d9f14ec 100644
--- a/fs/operations/check.go
+++ b/fs/operations/check.go
@@ -335,7 +335,8 @@ func CheckIdenticalDownload(ctx context.Context, dst, src fs.Object) (differ boo
 
 // Does the work for CheckIdenticalDownload
 func checkIdenticalDownload(ctx context.Context, dst, src fs.Object) (differ bool, err error) {
-	in1, err := Open(ctx, dst)
+	var in1, in2 io.ReadCloser
+	in1, err = Open(ctx, dst)
 	if err != nil {
 		return true, fmt.Errorf("failed to open %q: %w", dst, err)
 	}
@@ -345,7 +346,7 @@ func checkIdenticalDownload(ctx context.Context, dst, src fs.Object) (differ boo
 	}()
 	in1 = tr1.Account(ctx, in1).WithBuffer() // account and buffer the transfer
 
-	in2, err := Open(ctx, src)
+	in2, err = Open(ctx, src)
 	if err != nil {
 		return true, fmt.Errorf("failed to open %q: %w", src, err)
 	}
diff --git a/fs/operations/operations.go b/fs/operations/operations.go
index 8fb55c184..a7e2f6d50 100644
--- a/fs/operations/operations.go
+++ b/fs/operations/operations.go
@@ -771,7 +771,8 @@ func hashSum(ctx context.Context, ht hash.Type, base64Encoded bool, downloadFlag
 		for _, option := range fs.GetConfig(ctx).DownloadHeaders {
 			options = append(options, option)
 		}
-		in, err := Open(ctx, o, options...)
+		var in io.ReadCloser
+		in, err = Open(ctx, o, options...)
 		if err != nil {
 			return "ERROR", fmt.Errorf("failed to open file %v: %w", o, err)
 		}
@@ -1071,7 +1072,8 @@ func Cat(ctx context.Context, f fs.Fs, w io.Writer, offset, count int64, sep []b
 		for _, option := range ci.DownloadHeaders {
 			options = append(options, option)
 		}
-		in, err := Open(ctx, o, options...)
+		var in io.ReadCloser
+		in, err = Open(ctx, o, options...)
 		if err != nil {
 			err = fs.CountError(err)
 			fs.Errorf(o, "Failed to open: %v", err)
diff --git a/fs/operations/reopen.go b/fs/operations/reopen.go
index 2e2a114ed..b2531ced0 100644
--- a/fs/operations/reopen.go
+++ b/fs/operations/reopen.go
@@ -10,23 +10,42 @@ import (
 	"github.com/rclone/rclone/fs/fserrors"
 )
 
+// AccountFn is a function which will be called after every read
+// from the ReOpen.
+//
+// It may return an error which will be passed back to the user.
+type AccountFn func(n int) error
+
 // ReOpen is a wrapper for an object reader which reopens the stream on error
 type ReOpen struct {
-	ctx      context.Context
-	mu       sync.Mutex      // mutex to protect the below
-	src      fs.Object       // object to open
-	options  []fs.OpenOption // option to pass to initial open
-	rc       io.ReadCloser   // underlying stream
-	read     int64           // number of bytes read from this stream
-	maxTries int             // maximum number of retries
-	tries    int             // number of retries we've had so far in this stream
-	err      error           // if this is set then Read/Close calls will return it
-	opened   bool            // if set then rc is valid and needs closing
+	ctx         context.Context
+	mu          sync.Mutex      // mutex to protect the below
+	src         fs.Object       // object to open
+	baseOptions []fs.OpenOption // options to pass to initial open and where offset == 0
+	options     []fs.OpenOption // option to pass on subsequent opens where offset != 0
+	rangeOption fs.RangeOption  // adjust this range option on re-opens
+	rc          io.ReadCloser   // underlying stream
+	size        int64           // total size of object - can be -ve
+	start       int64           // absolute position to start reading from
+	end         int64           // absolute position to end reading (exclusive)
+	offset      int64           // offset in the file we are at, offset from start
+	newOffset   int64           // if different to offset, reopen needed
+	maxTries    int             // maximum number of retries
+	tries       int             // number of retries we've had so far in this stream
+	err         error           // if this is set then Read/Close calls will return it
+	opened      bool            // if set then rc is valid and needs closing
+	account     AccountFn       // account for a read
+	reads       int             // count how many times the data has been read
+	accountOn   int             // only account on or after this read
 }
 
 var (
-	errorFileClosed   = errors.New("file already closed")
-	errorTooManyTries = errors.New("failed to reopen: too many retries")
+	errFileClosed    = errors.New("file already closed")
+	errTooManyTries  = errors.New("failed to reopen: too many retries")
+	errInvalidWhence = errors.New("reopen Seek: invalid whence")
+	errNegativeSeek  = errors.New("reopen Seek: negative position")
+	errSeekPastEnd   = errors.New("reopen Seek: attempt to seek past end of data")
+	errBadEndSeek    = errors.New("reopen Seek: can't seek from end with unknown sized object")
 )
 
 // NewReOpen makes a handle which will reopen itself and seek to where
@@ -37,15 +56,49 @@ var (
 //
 // If an fs.RangeOption is set then this will applied when reading from
 // the start, and updated on retries.
-func NewReOpen(ctx context.Context, src fs.Object, maxTries int, options ...fs.OpenOption) (rc io.ReadCloser, err error) {
+func NewReOpen(ctx context.Context, src fs.Object, maxTries int, options ...fs.OpenOption) (rc *ReOpen, err error) {
 	h := &ReOpen{
-		ctx:      ctx,
-		src:      src,
-		maxTries: maxTries,
-		options:  options,
+		ctx:         ctx,
+		src:         src,
+		maxTries:    maxTries,
+		baseOptions: options,
+		size:        src.Size(),
+		start:       0,
+		offset:      0,
+		newOffset:   -1, // -1 means no seek required
 	}
 	h.mu.Lock()
 	defer h.mu.Unlock()
+
+	// Filter the options for subsequent opens
+	h.options = make([]fs.OpenOption, 0, len(options)+1)
+	var limit int64 = -1
+	for _, option := range options {
+		switch x := option.(type) {
+		case *fs.HashesOption:
+			// leave hash option out when ranging
+		case *fs.RangeOption:
+			h.start, limit = x.Decode(h.end)
+		case *fs.SeekOption:
+			h.start, limit = x.Offset, -1
+		default:
+			h.options = append(h.options, option)
+		}
+	}
+
+	// Put our RangeOption on the end
+	h.rangeOption.Start = h.start
+	h.options = append(h.options, &h.rangeOption)
+
+	// If a size range is set then set the end point of the file to that
+	if limit >= 0 && h.size >= 0 {
+		h.end = h.start + limit
+		h.rangeOption.End = h.end - 1 // remember range options are inclusive
+	} else {
+		h.end = h.size
+		h.rangeOption.End = -1
+	}
+
 	err = h.open()
 	if err != nil {
 		return nil, err
@@ -66,7 +119,7 @@ func NewReOpen(ctx context.Context, src fs.Object, maxTries int, options ...fs.O
 // tries.
 //
 // Use this instead of calling the Open method on fs.Objects
-func Open(ctx context.Context, src fs.Object, options ...fs.OpenOption) (rc io.ReadCloser, err error) {
+func Open(ctx context.Context, src fs.Object, options ...fs.OpenOption) (rc *ReOpen, err error) {
 	maxTries := fs.GetConfig(ctx).LowLevelRetries
 	return NewReOpen(ctx, src, maxTries, options...)
 }
@@ -75,49 +128,25 @@ func Open(ctx context.Context, src fs.Object, options ...fs.OpenOption) (rc io.R
 //
 // we don't retry here as the Open() call will itself have low level retries
 func (h *ReOpen) open() error {
-	opts := []fs.OpenOption{}
-	var hashOption *fs.HashesOption
-	var rangeOption *fs.RangeOption
-	for _, option := range h.options {
-		switch option := option.(type) {
-		case *fs.HashesOption:
-			hashOption = option
-		case *fs.RangeOption:
-			rangeOption = option
-		case *fs.HTTPOption:
-			opts = append(opts, option)
-		default:
-			if option.Mandatory() {
-				fs.Logf(h.src, "Unsupported mandatory option: %v", option)
-			}
-		}
-	}
-	if h.read == 0 {
-		if rangeOption != nil {
-			opts = append(opts, rangeOption)
-		}
-		if hashOption != nil {
-			// put hashOption on if reading from the start, ditch otherwise
-			opts = append(opts, hashOption)
-		}
+	var opts []fs.OpenOption
+	if h.offset == 0 {
+		// if reading from the start using the initial options
+		opts = h.baseOptions
 	} else {
-		if rangeOption != nil {
-			// range to the read point
-			opts = append(opts, &fs.RangeOption{Start: rangeOption.Start + h.read, End: rangeOption.End})
-		} else {
-			// seek to the read point
-			opts = append(opts, &fs.SeekOption{Offset: h.read})
-		}
+		// otherwise use the filtered options
+		opts = h.options
+		// Adjust range start to where we have got to
+		h.rangeOption.Start = h.start + h.offset
 	}
 	h.tries++
 	if h.tries > h.maxTries {
-		h.err = errorTooManyTries
+		h.err = errTooManyTries
 	} else {
 		h.rc, h.err = h.src.Open(h.ctx, opts...)
 	}
 	if h.err != nil {
 		if h.tries > 1 {
-			fs.Debugf(h.src, "Reopen failed after %d bytes read: %v", h.read, h.err)
+			fs.Debugf(h.src, "Reopen failed after offset %d bytes read: %v", h.offset, h.err)
 		}
 		return h.err
 	}
@@ -125,6 +154,31 @@ func (h *ReOpen) open() error {
 	return nil
 }
 
+// reopen the underlying handle by closing it and reopening it.
+func (h *ReOpen) reopen() (err error) {
+	// close underlying stream if needed
+	if h.opened {
+		h.opened = false
+		_ = h.rc.Close()
+	}
+	return h.open()
+}
+
+// account for n bytes being read
+func (h *ReOpen) accountRead(n int) error {
+	if h.account == nil {
+		return nil
+	}
+	// Don't start accounting until we've reached this many reads
+	//
+	// rw.reads will be 1 the first time this is called
+	// rw.accountOn 2 means start accounting on the 2nd read through
+	if h.reads >= h.accountOn {
+		return h.account(n)
+	}
+	return nil
+}
+
 // Read bytes retrying as necessary
 func (h *ReOpen) Read(p []byte) (n int, err error) {
 	h.mu.Lock()
@@ -133,32 +187,128 @@ func (h *ReOpen) Read(p []byte) (n int, err error) {
 		// return a previous error if there is one
 		return n, h.err
 	}
-	n, err = h.rc.Read(p)
-	if err != nil {
-		h.err = err
+
+	// re-open if seek needed
+	if h.newOffset >= 0 {
+		if h.offset != h.newOffset {
+			fs.Debugf(h.src, "Seek from %d to %d", h.offset, h.newOffset)
+			h.offset = h.newOffset
+			err = h.reopen()
+			if err != nil {
+				return 0, err
+			}
+		}
+		h.newOffset = -1
 	}
-	h.read += int64(n)
-	if err != nil && err != io.EOF && !fserrors.IsNoLowLevelRetryError(err) {
-		// close underlying stream
-		h.opened = false
-		_ = h.rc.Close()
-		// reopen stream, clearing error if successful
-		fs.Debugf(h.src, "Reopening on read failure after %d bytes: retry %d/%d: %v", h.read, h.tries, h.maxTries, err)
-		if h.open() == nil {
-			err = nil
+
+	// Read a full buffer
+	startOffset := h.offset
+	var nn int
+	for n < len(p) && err == nil {
+		nn, err = h.rc.Read(p[n:])
+		n += nn
+		h.offset += int64(nn)
+		if err != nil && err != io.EOF {
+			h.err = err
+			if !fserrors.IsNoLowLevelRetryError(err) {
+				fs.Debugf(h.src, "Reopening on read failure after offset %d bytes: retry %d/%d: %v", h.offset, h.tries, h.maxTries, err)
+				if h.reopen() == nil {
+					err = nil
+				}
+			}
 		}
 	}
+	// Count a read of the data if we read from the start successfully
+	if startOffset == 0 && n != 0 {
+		h.reads++
+	}
+	// Account the read
+	accErr := h.accountRead(n)
+	if err == nil {
+		err = accErr
+	}
 	return n, err
 }
 
+// Seek sets the offset for the next Read or Write to offset, interpreted
+// according to whence: SeekStart means relative to the start of the file,
+// SeekCurrent means relative to the current offset, and SeekEnd means relative
+// to the end (for example, offset = -2 specifies the penultimate byte of the
+// file). Seek returns the new offset relative to the start of the file or an
+// error, if any.
+//
+// Seeking to an offset before the start of the file is an error. Seeking
+// to any positive offset may be allowed, but if the new offset exceeds the
+// size of the underlying object the behavior of subsequent I/O operations is
+// implementation-dependent.
+func (h *ReOpen) Seek(offset int64, whence int) (int64, error) {
+	h.mu.Lock()
+	defer h.mu.Unlock()
+	if h.err != nil {
+		// return a previous error if there is one
+		return 0, h.err
+	}
+	var abs int64
+	var size = h.end - h.start
+	switch whence {
+	case io.SeekStart:
+		abs = offset
+	case io.SeekCurrent:
+		if h.newOffset >= 0 {
+			abs = h.newOffset + offset
+		} else {
+			abs = h.offset + offset
+		}
+	case io.SeekEnd:
+		if h.size < 0 {
+			return 0, errBadEndSeek
+		}
+		abs = size + offset
+	default:
+		return 0, errInvalidWhence
+	}
+	if abs < 0 {
+		return 0, errNegativeSeek
+	}
+	if h.size >= 0 && abs > size {
+		return size, errSeekPastEnd
+	}
+
+	h.tries = 0       // Reset open count on seek
+	h.newOffset = abs // New offset - applied in Read
+	return abs, nil
+}
+
 // Close the stream
 func (h *ReOpen) Close() error {
 	h.mu.Lock()
 	defer h.mu.Unlock()
 	if !h.opened {
-		return errorFileClosed
+		return errFileClosed
 	}
 	h.opened = false
-	h.err = errorFileClosed
+	h.err = errFileClosed
 	return h.rc.Close()
 }
+
+// SetAccounting should be provided with a function which will be
+// called after every read from the RW.
+//
+// It may return an error which will be passed back to the user.
+func (h *ReOpen) SetAccounting(account AccountFn) *ReOpen {
+	h.account = account
+	return h
+}
+
+// DelayAccounting makes sure the accounting function only gets called
+// on the i-th or later read of the data from this point (counting
+// from 1).
+//
+// This is useful so that we don't account initial reads of the data
+// e.g. when calculating hashes.
+//
+// Set this to 0 to account everything.
+func (h *ReOpen) DelayAccounting(i int) {
+	h.accountOn = i
+	h.reads = 0
+}
diff --git a/fs/operations/reopen_test.go b/fs/operations/reopen_test.go
index 2a7195b56..6cb42a439 100644
--- a/fs/operations/reopen_test.go
+++ b/fs/operations/reopen_test.go
@@ -9,12 +9,17 @@ import (
 	"github.com/rclone/rclone/fs"
 	"github.com/rclone/rclone/fs/hash"
 	"github.com/rclone/rclone/fstest/mockobject"
+	"github.com/rclone/rclone/lib/pool"
 	"github.com/rclone/rclone/lib/readers"
 	"github.com/stretchr/testify/assert"
+	"github.com/stretchr/testify/require"
 )
 
-// check interface
-var _ io.ReadCloser = (*ReOpen)(nil)
+// check interfaces
+var (
+	_ io.ReadSeekCloser      = (*ReOpen)(nil)
+	_ pool.DelayAccountinger = (*ReOpen)(nil)
+)
 
 var errorTestError = errors.New("test error")
 
@@ -24,13 +29,36 @@ var errorTestError = errors.New("test error")
 // error
 type reOpenTestObject struct {
 	fs.Object
-	breaks []int64
+	t           *testing.T
+	breaks      []int64
+	unknownSize bool
 }
 
 // Open opens the file for read.  Call Close() on the returned io.ReadCloser
 //
 // This will break after reading the number of bytes in breaks
 func (o *reOpenTestObject) Open(ctx context.Context, options ...fs.OpenOption) (io.ReadCloser, error) {
+	gotHash := false
+	gotRange := false
+	startPos := int64(0)
+	for _, option := range options {
+		switch x := option.(type) {
+		case *fs.HashesOption:
+			gotHash = true
+		case *fs.RangeOption:
+			gotRange = true
+			startPos = x.Start
+			if o.unknownSize {
+				assert.Equal(o.t, int64(-1), x.End)
+			}
+		case *fs.SeekOption:
+			startPos = x.Offset
+		}
+	}
+	// Check if ranging, mustn't have hash if offset != 0
+	if gotHash && gotRange {
+		assert.Equal(o.t, int64(0), startPos)
+	}
 	rc, err := o.Object.Open(ctx, options...)
 	if err != nil {
 		return nil, err
@@ -52,28 +80,53 @@ func (o *reOpenTestObject) Open(ctx context.Context, options ...fs.OpenOption) (
 }
 
 func TestReOpen(t *testing.T) {
-	for testIndex, testName := range []string{"Seek", "Range"} {
+	for _, testName := range []string{"Normal", "WithRangeOption", "WithSeekOption", "UnknownSize"} {
 		t.Run(testName, func(t *testing.T) {
 			// Contents for the mock object
 			var (
 				reOpenTestcontents = []byte("0123456789")
 				expectedRead       = reOpenTestcontents
 				rangeOption        *fs.RangeOption
+				seekOption         *fs.SeekOption
+				unknownSize        = false
 			)
-			if testIndex > 0 {
-				rangeOption = &fs.RangeOption{Start: 1, End: 7}
+			switch testName {
+			case "Normal":
+			case "WithRangeOption":
+				rangeOption = &fs.RangeOption{Start: 1, End: 7} // range is inclusive
 				expectedRead = reOpenTestcontents[1:8]
+			case "WithSeekOption":
+				seekOption = &fs.SeekOption{Offset: 2}
+				expectedRead = reOpenTestcontents[2:]
+			case "UnknownSize":
+				rangeOption = &fs.RangeOption{Start: 1, End: -1}
+				expectedRead = reOpenTestcontents[1:]
+				unknownSize = true
+			default:
+				panic("bad test name")
 			}
 
 			// Start the test with the given breaks
-			testReOpen := func(breaks []int64, maxRetries int) (io.ReadCloser, error) {
+			testReOpen := func(breaks []int64, maxRetries int) (*ReOpen, error) {
 				srcOrig := mockobject.New("potato").WithContent(reOpenTestcontents, mockobject.SeekModeNone)
+				srcOrig.SetUnknownSize(unknownSize)
 				src := &reOpenTestObject{
-					Object: srcOrig,
-					breaks: breaks,
+					Object:      srcOrig,
+					t:           t,
+					breaks:      breaks,
+					unknownSize: unknownSize,
 				}
-				hashOption := &fs.HashesOption{Hashes: hash.NewHashSet(hash.MD5)}
-				return NewReOpen(context.Background(), src, maxRetries, hashOption, rangeOption)
+				opts := []fs.OpenOption{}
+				if rangeOption == nil && seekOption == nil {
+					opts = append(opts, &fs.HashesOption{Hashes: hash.NewHashSet(hash.MD5)})
+				}
+				if rangeOption != nil {
+					opts = append(opts, rangeOption)
+				}
+				if seekOption != nil {
+					opts = append(opts, seekOption)
+				}
+				return NewReOpen(context.Background(), src, maxRetries, opts...)
 			}
 
 			t.Run("Basics", func(t *testing.T) {
@@ -92,16 +145,25 @@ func TestReOpen(t *testing.T) {
 				assert.Equal(t, 0, n)
 				assert.Equal(t, io.EOF, err)
 
+				// Rewind the stream
+				_, err = h.Seek(0, io.SeekStart)
+				require.NoError(t, err)
+
+				// Check contents read correctly
+				got, err = io.ReadAll(h)
+				assert.NoError(t, err)
+				assert.Equal(t, expectedRead, got)
+
 				// Check close
 				assert.NoError(t, h.Close())
 
 				// Check double close
-				assert.Equal(t, errorFileClosed, h.Close())
+				assert.Equal(t, errFileClosed, h.Close())
 
 				// Check read after close
 				n, err = h.Read(buf)
 				assert.Equal(t, 0, n)
-				assert.Equal(t, errorFileClosed, err)
+				assert.Equal(t, errFileClosed, err)
 			})
 
 			t.Run("ErrorAtStart", func(t *testing.T) {
@@ -139,10 +201,176 @@ func TestReOpen(t *testing.T) {
 				var buf = make([]byte, 1)
 				n, err := h.Read(buf)
 				assert.Equal(t, 0, n)
-				assert.Equal(t, errorTooManyTries, err)
+				assert.Equal(t, errTooManyTries, err)
 
 				// Check close
-				assert.Equal(t, errorFileClosed, h.Close())
+				assert.Equal(t, errFileClosed, h.Close())
+			})
+
+			t.Run("Seek", func(t *testing.T) {
+				// open
+				h, err := testReOpen([]int64{2, 1, 3}, 10)
+				assert.NoError(t, err)
+
+				// Seek to end
+				pos, err := h.Seek(int64(len(expectedRead)), io.SeekStart)
+				assert.NoError(t, err)
+				assert.Equal(t, int64(len(expectedRead)), pos)
+
+				// Seek to start
+				pos, err = h.Seek(0, io.SeekStart)
+				assert.NoError(t, err)
+				assert.Equal(t, int64(0), pos)
+
+				// Should not allow seek past end
+				pos, err = h.Seek(int64(len(expectedRead))+1, io.SeekCurrent)
+				if !unknownSize {
+					assert.Equal(t, errSeekPastEnd, err)
+					assert.Equal(t, len(expectedRead), int(pos))
+				} else {
+					assert.Equal(t, nil, err)
+					assert.Equal(t, len(expectedRead)+1, int(pos))
+
+					// Seek back to start to get tests in sync
+					pos, err = h.Seek(0, io.SeekStart)
+					assert.NoError(t, err)
+					assert.Equal(t, int64(0), pos)
+				}
+
+				// Should not allow seek to negative position start
+				pos, err = h.Seek(-1, io.SeekCurrent)
+				assert.Equal(t, errNegativeSeek, err)
+				assert.Equal(t, 0, int(pos))
+
+				// Should not allow seek with invalid whence
+				pos, err = h.Seek(0, 3)
+				assert.Equal(t, errInvalidWhence, err)
+				assert.Equal(t, 0, int(pos))
+
+				// check read
+				dst := make([]byte, 5)
+				n, err := h.Read(dst)
+				assert.Nil(t, err)
+				assert.Equal(t, 5, n)
+				assert.Equal(t, expectedRead[:5], dst)
+
+				// Test io.SeekCurrent
+				pos, err = h.Seek(-3, io.SeekCurrent)
+				assert.Nil(t, err)
+				assert.Equal(t, 2, int(pos))
+
+				// check read
+				n, err = h.Read(dst)
+				assert.Nil(t, err)
+				assert.Equal(t, 5, n)
+				assert.Equal(t, expectedRead[2:7], dst)
+
+				pos, err = h.Seek(-2, io.SeekCurrent)
+				assert.Nil(t, err)
+				assert.Equal(t, 5, int(pos))
+
+				// Test io.SeekEnd
+				pos, err = h.Seek(-3, io.SeekEnd)
+				if !unknownSize {
+					assert.Nil(t, err)
+					assert.Equal(t, len(expectedRead)-3, int(pos))
+				} else {
+					assert.Equal(t, errBadEndSeek, err)
+					assert.Equal(t, 0, int(pos))
+
+					// sync
+					pos, err = h.Seek(1, io.SeekCurrent)
+					assert.Nil(t, err)
+					assert.Equal(t, 6, int(pos))
+				}
+
+				// check read
+				dst = make([]byte, 3)
+				n, err = h.Read(dst)
+				assert.Nil(t, err)
+				assert.Equal(t, 3, n)
+				assert.Equal(t, expectedRead[len(expectedRead)-3:], dst)
+
+				// check close
+				assert.NoError(t, h.Close())
+				_, err = h.Seek(0, io.SeekCurrent)
+				assert.Equal(t, errFileClosed, err)
+			})
+
+			t.Run("AccountRead", func(t *testing.T) {
+				h, err := testReOpen(nil, 10)
+				assert.NoError(t, err)
+
+				var total int
+				h.SetAccounting(func(n int) error {
+					total += n
+					return nil
+				})
+
+				dst := make([]byte, 3)
+				n, err := h.Read(dst)
+				assert.Equal(t, 3, n)
+				assert.NoError(t, err)
+				assert.Equal(t, 3, total)
+			})
+
+			t.Run("AccountReadDelay", func(t *testing.T) {
+				h, err := testReOpen(nil, 10)
+				assert.NoError(t, err)
+
+				var total int
+				h.SetAccounting(func(n int) error {
+					total += n
+					return nil
+				})
+
+				rewind := func() {
+					_, err := h.Seek(0, io.SeekStart)
+					require.NoError(t, err)
+				}
+
+				h.DelayAccounting(3)
+
+				dst := make([]byte, 16)
+
+				n, err := h.Read(dst)
+				assert.Equal(t, len(expectedRead), n)
+				assert.Equal(t, io.EOF, err)
+				assert.Equal(t, 0, total)
+				rewind()
+
+				n, err = h.Read(dst)
+				assert.Equal(t, len(expectedRead), n)
+				assert.Equal(t, io.EOF, err)
+				assert.Equal(t, 0, total)
+				rewind()
+
+				n, err = h.Read(dst)
+				assert.Equal(t, len(expectedRead), n)
+				assert.Equal(t, io.EOF, err)
+				assert.Equal(t, len(expectedRead), total)
+				rewind()
+
+				n, err = h.Read(dst)
+				assert.Equal(t, len(expectedRead), n)
+				assert.Equal(t, io.EOF, err)
+				assert.Equal(t, 2*len(expectedRead), total)
+				rewind()
+			})
+
+			t.Run("AccountReadError", func(t *testing.T) {
+				// Test accounting errors
+				h, err := testReOpen(nil, 10)
+				assert.NoError(t, err)
+
+				h.SetAccounting(func(n int) error {
+					return errorTestError
+				})
+
+				dst := make([]byte, 3)
+				n, err := h.Read(dst)
+				assert.Equal(t, 3, n)
+				assert.Equal(t, errorTestError, err)
 			})
 		})
 	}