diff --git a/b2/b2.go b/b2/b2.go
index cbdfc9e79..152c8fddf 100644
--- a/b2/b2.go
+++ b/b2/b2.go
@@ -5,6 +5,7 @@ package b2
 // checking SHA1s?
 
 import (
+	"bufio"
 	"bytes"
 	"crypto/sha1"
 	"fmt"
@@ -705,6 +706,11 @@ func (f *Fs) Put(in io.Reader, src fs.ObjectInfo, options ...fs.OpenOption) (fs.
 	return fs, fs.Update(in, src, options...)
 }
 
+// PutStream uploads to the remote path with the modTime given of indeterminate size
+func (f *Fs) PutStream(in io.Reader, src fs.ObjectInfo, options ...fs.OpenOption) (fs.Object, error) {
+	return f.Put(in, src, options...)
+}
+
 // Mkdir creates the bucket if it doesn't exist
 func (f *Fs) Mkdir(dir string) error {
 	f.bucketOKMu.Lock()
@@ -1237,8 +1243,33 @@ func (o *Object) Update(in io.Reader, src fs.ObjectInfo, options ...fs.OpenOptio
 	}
 	size := src.Size()
 
-	// If a large file upload in chunks - see upload.go
-	if size >= int64(uploadCutoff) {
+	if size == -1 {
+		// Check if the file is large enough for a chunked upload (needs to be at least two chunks)
+		buf := o.fs.getUploadBlock()
+		n, err := io.ReadFull(in, buf)
+		if err == nil {
+			bufReader := bufio.NewReader(in)
+			in = bufReader
+			_, err = bufReader.Peek(1)
+		}
+
+		if err == nil {
+			fs.Debugf(o, "File is big enough for chunked streaming")
+			up, err := o.fs.newLargeUpload(o, in, src)
+			if err != nil {
+				o.fs.putUploadBlock(buf)
+				return err
+			}
+			return up.Stream(buf)
+		} else if err == io.EOF || err == io.ErrUnexpectedEOF {
+			fs.Debugf(o, "File has %d bytes, which makes only one chunk. Using direct upload.", n)
+			defer o.fs.putUploadBlock(buf)
+			size = int64(n)
+			in = bytes.NewReader(buf[:n])
+		} else {
+			return err
+		}
+	} else if size > int64(uploadCutoff) {
 		up, err := o.fs.newLargeUpload(o, in, src)
 		if err != nil {
 			return err
@@ -1373,10 +1404,11 @@ func (o *Object) MimeType() string {
 
 // Check the interfaces are satisfied
 var (
-	_ fs.Fs         = &Fs{}
-	_ fs.Purger     = &Fs{}
-	_ fs.CleanUpper = &Fs{}
-	_ fs.ListRer    = &Fs{}
-	_ fs.Object     = &Object{}
-	_ fs.MimeTyper  = &Object{}
+	_ fs.Fs          = &Fs{}
+	_ fs.Purger      = &Fs{}
+	_ fs.PutStreamer = &Fs{}
+	_ fs.CleanUpper  = &Fs{}
+	_ fs.ListRer     = &Fs{}
+	_ fs.Object      = &Object{}
+	_ fs.MimeTyper   = &Object{}
 )
diff --git a/b2/upload.go b/b2/upload.go
index a803991b3..dbf53731e 100644
--- a/b2/upload.go
+++ b/b2/upload.go
@@ -70,7 +70,7 @@ type largeUpload struct {
 	in       io.Reader                       // read the data from here
 	id       string                          // ID of the file being uploaded
 	size     int64                           // total size
-	parts    int64                           // calculated number of parts
+	parts    int64                           // calculated number of parts, if known
 	sha1s    []string                        // slice of SHA1s for each part
 	uploadMu sync.Mutex                      // lock for upload variable
 	uploads  []*api.GetUploadPartURLResponse // result of get upload URL calls
@@ -80,13 +80,21 @@ type largeUpload struct {
 func (f *Fs) newLargeUpload(o *Object, in io.Reader, src fs.ObjectInfo) (up *largeUpload, err error) {
 	remote := o.remote
 	size := src.Size()
-	parts := size / int64(chunkSize)
-	if size%int64(chunkSize) != 0 {
-		parts++
-	}
-	if parts > maxParts {
-		return nil, errors.Errorf("%q too big (%d bytes) makes too many parts %d > %d - increase --b2-chunk-size", remote, size, parts, maxParts)
+	parts := int64(0)
+	sha1SliceSize := int64(maxParts)
+	if size == -1 {
+		fs.Debugf(o, "Streaming upload with --b2-chunk-size %s allows uploads of up to %s and will fail only when that limit is reached.", fs.SizeSuffix(chunkSize), fs.SizeSuffix(maxParts*chunkSize))
+	} else {
+		parts = size / int64(chunkSize)
+		if size%int64(chunkSize) != 0 {
+			parts++
+		}
+		if parts > maxParts {
+			return nil, errors.Errorf("%q too big (%d bytes) makes too many parts %d > %d - increase --b2-chunk-size", remote, size, parts, maxParts)
+		}
+		sha1SliceSize = parts
 	}
+
 	modTime := src.ModTime()
 	opts := rest.Opts{
 		Method: "POST",
@@ -123,7 +131,7 @@ func (f *Fs) newLargeUpload(o *Object, in io.Reader, src fs.ObjectInfo) (up *lar
 		id:    response.ID,
 		size:  size,
 		parts: parts,
-		sha1s: make([]string, parts),
+		sha1s: make([]string, sha1SliceSize),
 	}
 	return up, nil
 }
@@ -243,6 +251,7 @@ func (up *largeUpload) transferChunk(part int64, body []byte) error {
 
 // finish closes off the large upload
 func (up *largeUpload) finish() error {
+	fs.Debugf(up.o, "Finishing large file upload with %d parts", up.parts)
 	opts := rest.Opts{
 		Method: "POST",
 		Path:   "/b2_finish_large_file",
@@ -279,6 +288,101 @@ func (up *largeUpload) cancel() error {
 	return err
 }
 
+func (up *largeUpload) managedTransferChunk(wg *sync.WaitGroup, errs chan error, part int64, buf []byte) {
+	wg.Add(1)
+	go func(part int64, buf []byte) {
+		defer wg.Done()
+		defer up.f.putUploadBlock(buf)
+		err := up.transferChunk(part, buf)
+		if err != nil {
+			select {
+			case errs <- err:
+			default:
+			}
+		}
+	}(part, buf)
+}
+
+func (up *largeUpload) finishOrCancelOnError(err error, errs chan error) error {
+	if err == nil {
+		select {
+		case err = <-errs:
+		default:
+		}
+	}
+	if err != nil {
+		fs.Debugf(up.o, "Cancelling large file upload due to error: %v", err)
+		cancelErr := up.cancel()
+		if cancelErr != nil {
+			fs.Errorf(up.o, "Failed to cancel large file upload: %v", cancelErr)
+		}
+		return err
+	}
+	return up.finish()
+}
+
+// Stream uploads the chunks from the input, starting with a required initial
+// chunk. Assumes the file size is unknown and will upload until the input
+// reaches EOF.
+func (up *largeUpload) Stream(initialUploadBlock []byte) (err error) {
+	fs.Debugf(up.o, "Starting streaming of large file (id %q)", up.id)
+	errs := make(chan error, 1)
+	hasMoreParts := true
+	var wg sync.WaitGroup
+	fs.AccountByPart(up.o) // Cancel whole file accounting before reading
+
+	// Transfer initial chunk
+	up.size = int64(len(initialUploadBlock))
+	up.managedTransferChunk(&wg, errs, 1, initialUploadBlock)
+
+outer:
+	for part := int64(2); hasMoreParts; part++ {
+		// Check any errors
+		select {
+		case err = <-errs:
+			break outer
+		default:
+		}
+
+		// Get a block of memory
+		buf := up.f.getUploadBlock()
+
+		// Read the chunk
+		n, err := io.ReadFull(up.in, buf)
+		if err == io.ErrUnexpectedEOF {
+			fs.Debugf(up.o, "Read less than a full chunk, making this the last one.")
+			buf = buf[:n]
+			hasMoreParts = false
+			err = nil
+		} else if err == io.EOF {
+			fs.Debugf(up.o, "Could not read any more bytes, previous chunk was the last.")
+			up.f.putUploadBlock(buf)
+			hasMoreParts = false
+			err = nil
+			break outer
+		} else if err != nil {
+			// other kinds of errors indicate failure
+			up.f.putUploadBlock(buf)
+			break outer
+		}
+
+		// Keep stats up to date
+		up.parts = part
+		up.size += int64(n)
+		if part > maxParts {
+			err = errors.Errorf("%q too big (%d bytes so far) makes too many parts %d > %d - increase --b2-chunk-size", up.o, up.size, up.parts, maxParts)
+			break outer
+		}
+
+		// Transfer the chunk
+		up.managedTransferChunk(&wg, errs, part, buf)
+	}
+	wg.Wait()
+	up.sha1s = up.sha1s[:up.parts]
+
+	return up.finishOrCancelOnError(err, errs)
+}
+
 // Upload uploads the chunks from the input
 func (up *largeUpload) Upload() error {
 	fs.Debugf(up.o, "Starting upload of large file in %d chunks (id %q)", up.parts, up.id)
@@ -312,37 +416,10 @@ outer:
 		}
 
 		// Transfer the chunk
-		wg.Add(1)
-		go func(part int64, buf []byte) {
-			defer wg.Done()
-			defer up.f.putUploadBlock(buf)
-			err := up.transferChunk(part, buf)
-			if err != nil {
-				select {
-				case errs <- err:
-				default:
-				}
-			}
-		}(part, buf)
-
+		up.managedTransferChunk(&wg, errs, part, buf)
 		remaining -= reqSize
 	}
 	wg.Wait()
-	if err == nil {
-		select {
-		case err = <-errs:
-		default:
-		}
-	}
-	if err != nil {
-		fs.Debugf(up.o, "Cancelling large file upload due to error: %v", err)
-		cancelErr := up.cancel()
-		if cancelErr != nil {
-			fs.Errorf(up.o, "Failed to cancel large file upload: %v", cancelErr)
-		}
-		return err
-	}
-	// Check any errors
-	fs.Debugf(up.o, "Finishing large file upload")
-	return up.finish()
+
+	return up.finishOrCancelOnError(err, errs)
 }
diff --git a/fs/operations.go b/fs/operations.go
index b8ff3ec83..b80a03a0a 100644
--- a/fs/operations.go
+++ b/fs/operations.go
@@ -121,7 +121,7 @@ func Equal(src ObjectInfo, dst Object) bool {
 func equal(src ObjectInfo, dst Object, sizeOnly, checkSum bool) bool {
 	if !Config.IgnoreSize {
 		if src.Size() != dst.Size() {
-			Debugf(src, "Sizes differ")
+			Debugf(src, "Sizes differ (src %d vs dst %d)", src.Size(), dst.Size())
 			return false
 		}
 	}