diff --git a/nullseed.go b/nullseed.go
index d1ceecb..37c6d99 100644
--- a/nullseed.go
+++ b/nullseed.go
@@ -11,6 +11,7 @@ import (
 type nullChunkSeed struct {
 	id         ChunkID
 	blockfile  *os.File
+	blockLen   uint64
 	canReflink bool
 }
 
@@ -19,11 +20,17 @@ func newNullChunkSeed(dstFile string, blocksize uint64, max uint64) (*nullChunkS
 	if err != nil {
 		return nil, err
 	}
-	var canReflink bool
+	var (
+		canReflink bool
+		blockLen   uint64
+	)
 	if CanClone(dstFile, blockfile.Name()) {
 		canReflink = true
-		b := make([]byte, blocksize)
-		if _, err := blockfile.Write(b); err != nil {
+		// Make the file of zeros as large as the largest chunk, rounded up to
+		// full blocks, so a run of zeros is cloned in few large pieces rather
+		// than one block at a time.
+		blockLen = (max + blocksize - 1) / blocksize * blocksize
+		if _, err := blockfile.Write(make([]byte, blockLen)); err != nil {
 			return nil, err
 		}
 	}
@@ -31,6 +38,7 @@ func newNullChunkSeed(dstFile string, blocksize uint64, max uint64) (*nullChunkS
 		id:         NewNullChunk(max).ID,
 		canReflink: canReflink,
 		blockfile:  blockfile,
+		blockLen:   blockLen,
 	}, nil
 }
 
@@ -69,6 +77,7 @@ func (s *nullChunkSeed) LongestMatchWith(chunks []IndexChunk) (int, SeedSegment)
 		from:       chunks[0].Start,
 		to:         chunks[n-1].Start + chunks[n-1].Size,
 		blockfile:  s.blockfile,
+		blockLen:   s.blockLen,
 		canReflink: s.canReflink,
 	}
 }
@@ -89,6 +98,7 @@ func (s *nullChunkSeed) IsInvalid() bool {
 type nullChunkSection struct {
 	from, to   uint64
 	blockfile  *os.File
+	blockLen   uint64 // Length of the blockfile, a multiple of the blocksize
 	canReflink bool
 }
 
@@ -155,15 +165,17 @@ func (s *nullChunkSection) clone(dst *os.File, offset, length, blocksize uint64)
 	}
 	copied += c2
 
-	for blkOffset := dstAlignStart; blkOffset < dstAlignEnd; blkOffset += blocksize {
-		if err := cloneRange(dst, s.blockfile, 0, blocksize, blkOffset); err != nil {
+	for blkOffset := dstAlignStart; blkOffset < dstAlignEnd; {
+		n := min(s.blockLen, dstAlignEnd-blkOffset)
+		if err := cloneRange(dst, s.blockfile, 0, n, blkOffset); err != nil {
 			// Not every filesystem that passes the CanClone probe can clone
 			// every range. ZFS for example refuses to clone from the blockfile
 			// before it has been committed to disk. Fall back to writing zeros.
 			c3, _, err := s.copy(dst, blkOffset, dstAlignEnd-blkOffset)
 			return copied + c3, cloned, err
 		}
-		cloned += blocksize
+		cloned += n
+		blkOffset += n
 	}
 	return copied, cloned, nil
 }
diff --git a/nullseed_test.go b/nullseed_test.go
index eac8692..b5f6c0d 100644
--- a/nullseed_test.go
+++ b/nullseed_test.go
@@ -29,7 +29,7 @@ func TestNullChunkSectionCloneFallback(t *testing.T) {
 	require.NoError(t, err)
 
 	newSection := func() *nullChunkSection {
-		return &nullChunkSection{from: 0, to: length, blockfile: blockfile, canReflink: true}
+		return &nullChunkSection{from: 0, to: length, blockfile: blockfile, blockLen: blocksize, canReflink: true}
 	}
 
 	t.Run("copies zeros when cloning fails", func(t *testing.T) {
@@ -92,7 +92,7 @@ func TestNullChunkSectionCloneFallback(t *testing.T) {
 		require.NoError(t, err)
 		defer dst.Close()
 
-		section := &nullChunkSection{from: from, to: from + sectionLen, blockfile: blockfile, canReflink: true}
+		section := &nullChunkSection{from: from, to: from + sectionLen, blockfile: blockfile, blockLen: blocksize, canReflink: true}
 		copied, cloned, err := section.WriteInto(dst, from, sectionLen, bigBlock, false)
 		require.NoError(t, err)
 		assert.Equal(t, uint64(0), cloned)
@@ -133,3 +133,54 @@ func TestNullChunkSectionCloneFallback(t *testing.T) {
 		assert.Equal(t, make([]byte, length), got)
 	})
 }
+
+// A run of zeros is cloned in pieces as large as the blockfile, with the
+// last piece shorter, rather than one block at a time.
+func TestNullChunkSectionClonesLargePieces(t *testing.T) {
+	defer func() { cloneRange = CloneRange }()
+
+	const (
+		blocksize = 4096
+		blockLen  = 4 * blocksize
+	)
+	dir := t.TempDir()
+	blockfile, err := os.CreateTemp(dir, ".tmp-block")
+	require.NoError(t, err)
+	defer blockfile.Close()
+
+	type call struct{ srcOffset, length, dstOffset uint64 }
+	var calls []call
+	cloneRange = func(dst, src *os.File, srcOffset, srcLength, dstOffset uint64) error {
+		calls = append(calls, call{srcOffset, srcLength, dstOffset})
+		// Write the zeros a real clone would have produced
+		_, err := dst.WriteAt(make([]byte, srcLength), int64(dstOffset))
+		return err
+	}
+
+	// Starts 100 bytes into the first block and covers 9 full blocks after it
+	from := uint64(100)
+	length := uint64(blocksize - from + 9*blocksize + 50)
+	fileLen := from + length + 1000
+	dstName := filepath.Join(dir, "out")
+	require.NoError(t, os.WriteFile(dstName, bytes.Repeat([]byte{0xff}, int(fileLen)), 0644))
+	dst, err := os.OpenFile(dstName, os.O_RDWR, 0)
+	require.NoError(t, err)
+	defer dst.Close()
+
+	section := &nullChunkSection{from: from, to: from + length, blockfile: blockfile, blockLen: blockLen, canReflink: true}
+	copied, cloned, err := section.WriteInto(dst, from, length, blocksize, false)
+	require.NoError(t, err)
+	assert.Equal(t, uint64(9*blocksize), cloned)
+	assert.Equal(t, length-9*blocksize, copied)
+	assert.Equal(t, []call{
+		{0, blockLen, blocksize},
+		{0, blockLen, 5 * blocksize},
+		{0, blocksize, 9 * blocksize},
+	}, calls)
+
+	got, err := os.ReadFile(dstName)
+	require.NoError(t, err)
+	assert.Equal(t, bytes.Repeat([]byte{0xff}, int(from)), got[:from])
+	assert.Equal(t, make([]byte, length), got[from:from+length])
+	assert.Equal(t, bytes.Repeat([]byte{0xff}, int(fileLen-from-length)), got[from+length:])
+}