diff --git a/internal/fusefrontend/file_holes.go b/internal/fusefrontend/file_holes.go
index 0d28004..cb44803 100644
--- a/internal/fusefrontend/file_holes.go
+++ b/internal/fusefrontend/file_holes.go
@@ -4,6 +4,7 @@ package fusefrontend
 
 import (
 	"context"
+	"runtime"
 	"syscall"
 
 	"github.com/hanwen/go-fuse/v2/fs"
@@ -57,12 +58,71 @@ func (f *File) zeroPad(plainSize uint64) syscall.Errno {
 }
 
 // Lseek - FUSE call.
+//
+// Looking at
+// fuse_file_llseek @ https://git.kernel.org/pub/scm/linux/kernel/git/stable/linux.git/tree/fs/fuse/file.c?h=v5.12.7#n2634
+// this function is only called for SEEK_HOLE & SEEK_DATA.
 func (f *File) Lseek(ctx context.Context, off uint64, whence uint32) (uint64, syscall.Errno) {
-	cipherOff := f.rootNode.contentEnc.PlainSizeToCipherSize(off)
-	newCipherOff, err := syscall.Seek(f.intFd(), int64(cipherOff), int(whence))
+	const (
+		SEEK_DATA = 3 // find next data segment at or above `off`
+		SEEK_HOLE = 4 // find next hole at or above `off`
+
+		// On error, we return -1 as the offset as per man lseek.
+		MinusOne = ^uint64(0)
+	)
+	if whence != SEEK_DATA && whence != SEEK_HOLE {
+		tlog.Warn.Printf("BUG: Lseek was called with whence=%d. This is not supported!", whence)
+		return 0, syscall.EINVAL
+	}
+	if runtime.GOOS != "linux" {
+		// MacOS has broken (different?) SEEK_DATA / SEEK_HOLE semantics, see
+		// https://lists.gnu.org/archive/html/bug-gnulib/2018-09/msg00051.html
+		tlog.Warn.Printf("buggy on non-linux platforms, disabling SEEK_DATA & SEEK_HOLE")
+		return MinusOne, syscall.ENOSYS
+	}
+
+	// We will need the file size
+	var st syscall.Stat_t
+	err := syscall.Fstat(f.intFd(), &st)
 	if err != nil {
 		return 0, fs.ToErrno(err)
 	}
-	newOff := f.contentEnc.CipherSizeToPlainSize(uint64(newCipherOff))
-	return newOff, 0
+	fileSize := st.Size
+	// Better safe than sorry. The logic is only tested for 4k blocks.
+	if st.Blksize != 4096 {
+		tlog.Warn.Printf("unsupported block size of %d bytes, disabling SEEK_DATA & SEEK_HOLE", st.Blksize)
+		return MinusOne, syscall.ENOSYS
+	}
+
+	// man lseek: offset beyond end of file -> ENXIO
+	if f.rootNode.contentEnc.PlainOffToCipherOff(off) >= uint64(fileSize) {
+		return MinusOne, syscall.ENXIO
+	}
+
+	// Round down to start of block:
+	cipherOff := f.rootNode.contentEnc.BlockNoToCipherOff(f.rootNode.contentEnc.PlainOffToBlockNo(off))
+	newCipherOff, err := syscall.Seek(f.intFd(), int64(cipherOff), int(whence))
+	if err != nil {
+		return MinusOne, fs.ToErrno(err)
+	}
+	// already in data/hole => return original offset
+	if newCipherOff == int64(cipherOff) {
+		return off, 0
+	}
+	// If there is no further hole, SEEK_HOLE returns the file size
+	// (SEEK_DATA returns ENXIO in this case).
+	if whence == SEEK_HOLE {
+		fi, err := f.fd.Stat()
+		if err != nil {
+			return MinusOne, fs.ToErrno(err)
+		}
+		if newCipherOff == fi.Size() {
+			return f.rootNode.contentEnc.CipherSizeToPlainSize(uint64(newCipherOff)), 0
+		}
+	}
+	// syscall.Seek gave us the beginning of the next ext4 data/hole section.
+	// The next gocryptfs data/hole block starts at the next block boundary,
+	// so we have to round up:
+	newBlockNo := f.rootNode.contentEnc.CipherOffToBlockNo(uint64(newCipherOff) + f.rootNode.contentEnc.CipherBS() - 1)
+	return f.rootNode.contentEnc.BlockNoToPlainOff(newBlockNo), 0
 }
diff --git a/tests/plaintextnames/file_holes_test.go b/tests/plaintextnames/file_holes_test.go
index d046cea..9948715 100644
--- a/tests/plaintextnames/file_holes_test.go
+++ b/tests/plaintextnames/file_holes_test.go
@@ -2,9 +2,12 @@ package plaintextnames
 
 import (
 	"fmt"
+	"math/rand"
 	"os"
 	"os/exec"
+	"syscall"
 	"testing"
+	"time"
 
 	"github.com/rfjakob/gocryptfs/tests/test_helpers"
 
@@ -26,38 +29,21 @@ func findHolesPretty(t *testing.T, path string) string {
 	return holes.PrettyPrint(segments)
 }
 
-// TestFileHoleCopy creates a sparse times, copies it a few times, and check if
-// the copies are the same (including the location of holes and data sections).
-//
-// The test runs with -plaintextnames because that makes it easier to manipulate
-// cipherdir directly.
-func TestFileHoleCopy(t *testing.T) {
-	n := "TestFileHoleCopy"
+func doTestFileHoleCopy(t *testing.T, name string, writeOffsets []int64) {
+	n := "TestFileHoleCopy." + name
 	pPath := []string{pDir + "/" + n}
 	cPath := []string{cDir + "/" + n}
 
-	f, err := os.Create(pPath[0])
-	if err != nil {
-		t.Fatal(err)
-	}
-	// | hole | x | hole | x | hole |
-	buf := []byte("x")
-	f.WriteAt(buf, 10000)
-	f.WriteAt(buf, 30000)
-	f.Truncate(50000)
-	f.Sync()
-	f.Close()
+	os.Remove(pPath[0])
+	holes.Create(pPath[0])
 
-	// You have to update this value manually when you change the sequence
-	// above
+	// expected md6
 	md5 := test_helpers.Md5fn(pPath[0])
-	if md5 != "4e8d0742bccfbcdbf1d71be688e4e81c" {
-		t.Fatalf("wrong md5: %s", md5)
-	}
 
 	pSegments := []string{findHolesPretty(t, pPath[0])}
 	cSegments := []string{findHolesPretty(t, cPath[0])}
 
+	// create 5 more copies
 	for i := 1; i < 5; i++ {
 		pPath = append(pPath, fmt.Sprintf("%s.%d", pPath[0], i))
 		cPath = append(cPath, fmt.Sprintf("%s.%d", cPath[0], i))
@@ -76,21 +62,90 @@ func TestFileHoleCopy(t *testing.T) {
 		cSegments = append(cSegments, findHolesPretty(t, cPath[i]))
 	}
 
+	// "cp --sparse=auto" checks of the file has fewer blocks on disk than it
+	// should have for its size. Only then it will try to create a sparse copy.
+	var st syscall.Stat_t
+	err := syscall.Stat(pPath[0], &st)
+	if err != nil {
+		t.Fatal(err)
+	}
+	// convert 512 byte blocks to 4k blocks
+	blocks4k := st.Blocks / 8
+	// For more than a few fragments, ext4 allocates one extra block
+	blocks4k++
+	if blocks4k >= (st.Size+4095)/4096 {
+		t.Logf("file will look non-sparse to cp, skipping segment check")
+		return
+	}
+
+	// Check that size on disk stays the same across copies
+	var st0 syscall.Stat_t
+	if err := syscall.Stat(pPath[0], &st0); err != nil {
+		t.Fatal(err)
+	}
 	for i := range pSegments {
-		t.Logf("pSegments[%d]: %s", i, pSegments[i])
+		var st syscall.Stat_t
+		if err := syscall.Stat(pPath[i], &st); err != nil {
+			t.Fatal(err)
+		}
+		// Sometimes the size on disk decreases by 4k due to less fragmentation
+		if st.Blocks != st0.Blocks && st.Blocks != st0.Blocks-8 {
+			t.Errorf("size changed: st0.Blocks=%d st%d.Blocks=%d", st0.Blocks, i, st.Blocks)
+		}
+	}
+
+	// Check that hole/data segments stays the same across copies
+	out := ""
+	same := true
+	for i := range pSegments {
+		out += fmt.Sprintf("pSegments[%d]:\n%s\n", i, pSegments[i])
 		if i < len(pSegments)-1 {
 			if pSegments[i+1] != pSegments[i] {
-				t.Errorf("error: this is different than pSegments[%d]!", i+1)
+				same = false
+				t.Errorf("error: pSegments[%d] is different than pSegments[%d]!", i, i+1)
 			}
 		}
 	}
-	t.Log("------------------------------------")
+	out += "------------------------------------\n"
 	for i := range cSegments {
-		t.Logf("cSegments[%d]: %s", i, cSegments[i])
+		out += fmt.Sprintf("cSegments[%d]:\n%s\n", i, cSegments[i])
 		if i < len(pSegments)-1 {
 			if cSegments[i+1] != cSegments[i] {
-				t.Errorf("error: this is different than cSegments[%d]!", i+1)
+				same = false
+				t.Errorf("error: cSegments[%d] is different than cSegments[%d]!", i, i+1)
 			}
 		}
 	}
+	if !same {
+		t.Log(out)
+	}
+}
+
+// TestFileHoleCopy creates a sparse times, copies it a few times, and check if
+// the copies are the same (including the location of holes and data sections).
+//
+// The test runs with -plaintextnames because that makes it easier to manipulate
+// cipherdir directly.
+func TestFileHoleCopy(t *testing.T) {
+	// | hole | x | hole | x | hole |
+	// truncate -s 50000 foo && dd if=/dev/zero of=foo bs=1 seek=10000 count=1 conv=notrunc && dd if=/dev/zero of=foo bs=1 seek=30000 count=1 conv=notrunc
+	name := "c0"
+	c0 := []int64{10000, 30000}
+	if !t.Run("c0", func(t *testing.T) { doTestFileHoleCopy(t, name, c0) }) {
+		t.Log("aborting further subtests")
+		return
+	}
+
+	rand.Seed(time.Now().UnixNano())
+	for k := 0; k < 100; k++ {
+		c1 := make([]int64, 10)
+		for i := range c1 {
+			c1[i] = int64(rand.Int31n(60000))
+		}
+		name := fmt.Sprintf("k%d", k)
+		if !t.Run(name, func(t *testing.T) { doTestFileHoleCopy(t, name, c1) }) {
+			t.Log("aborting further subtests")
+			return
+		}
+	}
 }