diff --git a/src/borg/chunkers/reader.pyx b/src/borg/chunkers/reader.pyx
index 26258914b9..9169ed3262 100644
--- a/src/borg/chunkers/reader.pyx
+++ b/src/borg/chunkers/reader.pyx
@@ -137,8 +137,11 @@ class FileFMAPReader:
         if self.try_sparse:
             try:
                 fmap = list(sparsemap(self.fd, self.fh))
-            except OSError as err:
-                # seeking did not work
+            except (OSError, ValueError) as err:
+                # Building a sparse map failed:
+                # - OSError: low-level lseek with SEEK_HOLE/SEEK_DATA not supported by FS/OS.
+                # - ValueError: high-level file objects (e.g. io.BytesIO or some fd wrappers)
+                #   don't accept SEEK_HOLE/SEEK_DATA as a valid "whence" and raise ValueError.
                 pass
 
         if fmap is None:
@@ -170,6 +173,9 @@ class FileFMAPReader:
                     # read block from the range
                     data = dread(offset, wanted, self.fd, self.fh)
                     got = len(data)
+                    # Detect zero-filled blocks regardless of sparse mode.
+                    # Zero detection is important to avoid reading/storing allocated zeros
+                    # even when we are not using sparse file handling based on SEEK_HOLE/SEEK_DATA.
                     if zeros.startswith(data):
                         data = None
                         allocation = CH_ALLOC
diff --git a/src/borg/testsuite/chunkers/__init__.py b/src/borg/testsuite/chunkers/__init__.py
index 2e01e98e33..ce9ff11e21 100644
--- a/src/borg/testsuite/chunkers/__init__.py
+++ b/src/borg/testsuite/chunkers/__init__.py
@@ -77,14 +77,38 @@ def fs_supports_sparse():
 BS = 4096  # filesystem block size
 
 # Some sparse files. X = content blocks, _ = sparse blocks.
+# Block size must always be BS.
+
 # X__XXX____
-map_sparse1 = [(0 * BS, 1 * BS, True), (1 * BS, 2 * BS, False), (3 * BS, 3 * BS, True), (6 * BS, 4 * BS, False)]
+map_sparse1 = [
+    (0, BS, True),
+    (1 * BS, BS, False),
+    (2 * BS, BS, False),
+    (3 * BS, BS, True),
+    (4 * BS, BS, True),
+    (5 * BS, BS, True),
+    (6 * BS, BS, False),
+    (7 * BS, BS, False),
+    (8 * BS, BS, False),
+    (9 * BS, BS, False),
+]
 
 # _XX___XXXX
-map_sparse2 = [(0 * BS, 1 * BS, False), (1 * BS, 2 * BS, True), (3 * BS, 3 * BS, False), (6 * BS, 4 * BS, True)]
+map_sparse2 = [
+    (0, BS, False),
+    (1 * BS, BS, True),
+    (2 * BS, BS, True),
+    (3 * BS, BS, False),
+    (4 * BS, BS, False),
+    (5 * BS, BS, False),
+    (6 * BS, BS, True),
+    (7 * BS, BS, True),
+    (8 * BS, BS, True),
+    (9 * BS, BS, True),
+]
 
 # XXX
-map_notsparse = [(0 * BS, 3 * BS, True)]
+map_notsparse = [(0, BS, True), (BS, BS, True), (2 * BS, BS, True)]
 
 # ___
-map_onlysparse = [(0 * BS, 3 * BS, False)]
+map_onlysparse = [(0, BS, False), (BS, BS, False), (2 * BS, BS, False)]
diff --git a/src/borg/testsuite/chunkers/fixed_test.py b/src/borg/testsuite/chunkers/fixed_test.py
index b8598a9266..a06d6bdb14 100644
--- a/src/borg/testsuite/chunkers/fixed_test.py
+++ b/src/borg/testsuite/chunkers/fixed_test.py
@@ -34,13 +34,15 @@
 )
 def test_chunkify_sparse(tmpdir, fname, sparse_map, header_size, sparse):
     def get_chunks(fname, sparse, header_size):
-        chunker = ChunkerFixed(4096, header_size=header_size, sparse=sparse)
+        chunker = ChunkerFixed(BS, header_size=header_size, sparse=sparse)
         with open(fname, "rb") as fd:
             return cf(chunker.chunkify(fd))
 
+    # this only works if sparse map blocks are same size as fixed chunker blocks
     fn = str(tmpdir / fname)
     make_sparsefile(fn, sparse_map, header_size=header_size)
-    get_chunks(fn, sparse=sparse, header_size=header_size) == make_content(sparse_map, header_size=header_size)
+    expected_content = make_content(sparse_map, header_size=header_size)
+    assert get_chunks(fn, sparse=sparse, header_size=header_size) == expected_content
 
 
 @pytest.mark.skipif("BORG_TESTS_SLOW" not in os.environ, reason="slow tests not enabled, use BORG_TESTS_SLOW=1")