diff --git a/src/journal/journald-file.c b/src/journal/journald-file.c
index 35ca305384..0e698e329b 100644
--- a/src/journal/journald-file.c
+++ b/src/journal/journald-file.c
@@ -179,7 +179,7 @@ static void journald_file_set_offline_internal(JournaldFile *f) {
 
                                 log_debug_errno(r, "Failed to re-enable copy-on-write for %s: %m, rewriting file", f->file->path);
 
-                                r = copy_file_atomic(f->file->path, f->file->path, f->file->mode, 0, FS_NOCOW_FL, COPY_REPLACE | COPY_FSYNC);
+                                r = copy_file_atomic(f->file->path, f->file->path, f->file->mode, 0, FS_NOCOW_FL, COPY_REPLACE | COPY_FSYNC | COPY_HOLES);
                                 if (r < 0) {
                                         log_debug_errno(r, "Failed to rewrite %s: %m", f->file->path);
                                         continue;
diff --git a/src/shared/copy.c b/src/shared/copy.c
index 1ace40424e..457488efa2 100644
--- a/src/shared/copy.c
+++ b/src/shared/copy.c
@@ -202,6 +202,46 @@ int copy_bytes_full(
                 if (max_bytes != UINT64_MAX && m > max_bytes)
                         m = max_bytes;
 
+                if (copy_flags & COPY_HOLES) {
+                        off_t c, e;
+
+                        c = lseek(fdf, 0, SEEK_CUR);
+                        if (c < 0)
+                                return -errno;
+
+                        /* To see if we're in a hole, we search for the next data offset. */
+                        e = lseek(fdf, c, SEEK_DATA);
+                        if (e < 0 && errno == ENXIO)
+                                /* If errno == ENXIO, that means we've reached the final hole of the file and
+                                * that hole isn't followed by more data. */
+                                e = lseek(fdf, 0, SEEK_END);
+                        if (e < 0)
+                                return -errno;
+
+                        /* If we're in a hole (current offset is not a data offset), create a hole of the
+                         * same size in the target file. */
+                        if (e > c && lseek(fdt, e - c, SEEK_CUR) < 0)
+                                return -errno;
+
+                        c = e; /* Set c to the start of the data segment. */
+
+                        /* After copying a potential hole, find the end of the data segment by looking for
+                         * the next hole. If we get ENXIO, we're at EOF. */
+                        e = lseek(fdf, c, SEEK_HOLE);
+                        if (e < 0) {
+                                if (errno == ENXIO)
+                                        break;
+                                return -errno;
+                        }
+
+                        /* SEEK_HOLE modifies the file offset so we need to move back to the initial offset. */
+                        if (lseek(fdf, c, SEEK_SET) < 0)
+                                return -errno;
+
+                        /* Make sure we're not copying more than the current data segment. */
+                        m = MIN(m, (size_t) e - c);
+                }
+
                 /* First try copy_file_range(), unless we already tried */
                 if (try_cfr) {
                         n = try_copy_file_range(fdf, NULL, fdt, NULL, m, 0u);
diff --git a/src/shared/copy.h b/src/shared/copy.h
index a7b45b4fbf..d755916bd9 100644
--- a/src/shared/copy.h
+++ b/src/shared/copy.h
@@ -24,6 +24,7 @@ typedef enum CopyFlags {
         COPY_FSYNC_FULL  = 1 << 11, /* fsync_full() after we are done */
         COPY_SYNCFS      = 1 << 12, /* syncfs() the *top-level* dir after we are done */
         COPY_ALL_XATTRS  = 1 << 13, /* Preserve all xattrs when copying, not just those in the user namespace */
+        COPY_HOLES       = 1 << 14, /* Copy holes */
 } CopyFlags;
 
 typedef int (*copy_progress_bytes_t)(uint64_t n_bytes, void *userdata);
diff --git a/src/test/test-copy.c b/src/test/test-copy.c
index c7ed054207..8572f25d87 100644
--- a/src/test/test-copy.c
+++ b/src/test/test-copy.c
@@ -323,4 +323,48 @@ TEST(copy_proc) {
         assert_se(!isempty(a));
 }
 
+TEST_RET(copy_holes) {
+        char fn[] = "/var/tmp/test-copy-hole-fd-XXXXXX";
+        char fn_copy[] = "/var/tmp/test-copy-hole-fd-XXXXXX";
+        struct stat stat;
+        int r, fd, fd_copy;
+
+        fd = mkostemp_safe(fn);
+        assert_se(fd >= 0);
+
+        fd_copy = mkostemp_safe(fn_copy);
+        assert_se(fd >= 0);
+
+        r = RET_NERRNO(fallocate(fd, FALLOC_FL_PUNCH_HOLE | FALLOC_FL_KEEP_SIZE, 0, 1));
+        if (ERRNO_IS_NOT_SUPPORTED(r))
+                return log_tests_skipped("Filesystem doesn't support hole punching");
+        assert_se(r >= 0);
+
+        /* We need to make sure to create a large enough hole and to write some data after it, otherwise
+         * filesystems (btrfs) might silently discard it. */
+
+        assert_se(lseek(fd, 1024 * 1024, SEEK_CUR) >= 0);
+        assert_se(write(fd, "abc", strlen("abc")) >= 0);
+        assert_se(lseek(fd, 0, SEEK_SET) >= 0);
+
+        assert_se(copy_bytes(fd, fd_copy, UINT64_MAX, COPY_HOLES) >= 0);
+
+        /* Test that the hole starts at the beginning of the file. */
+        assert_se(lseek(fd_copy, 0, SEEK_HOLE) == 0);
+        /* Test that the hole has the expected size. */
+        assert_se(lseek(fd_copy, 0, SEEK_DATA) == 1024 * 1024);
+
+        /* Test that the copied file has the correct size. */
+        assert_se(fstat(fd_copy, &stat) >= 0);
+        assert_se(stat.st_size == 1024 * 1024 + strlen("abc"));
+
+        close(fd);
+        close(fd_copy);
+
+        unlink(fn);
+        unlink(fn_copy);
+
+        return 0;
+}
+
 DEFINE_TEST_MAIN(LOG_DEBUG);