diff --git a/pooch/processors.py b/pooch/processors.py
index 4f775367..bbb2478b 100644
--- a/pooch/processors.py
+++ b/pooch/processors.py
@@ -23,6 +23,13 @@
 from .utils import get_logger
 
 
+def _is_selected_member(name, member):
+    """Check whether an archive entry is the member or its child."""
+    name = os.path.normpath(name)
+    member = os.path.normpath(member)
+    return name == member or name.startswith(member + os.path.sep)
+
+
 class ExtractorProcessor(abc.ABC):
     """
     Abstract base class for extractions from compressed archives.
@@ -132,7 +139,7 @@ def __call__(self, fname, action, pooch):  # noqa: ARG002
                     os.path.join(os.path.relpath(path, self.extract_dir), filename)
                 )
                 if self.members is None or any(
-                    relpath.startswith(os.path.normpath(m)) for m in self.members
+                    _is_selected_member(relpath, m) for m in self.members
                 ):
                     fnames.append(os.path.join(path, filename))
 
@@ -205,7 +212,7 @@ def _extract_file(self, fname, extract_dir):
                     subdir_members = [
                         name
                         for name in zip_file.namelist()
-                        if os.path.normpath(name).startswith(os.path.normpath(member))
+                        if _is_selected_member(name, member)
                     ]
                     # Extract the data file from within the archive
                     zip_file.extractall(members=subdir_members, path=extract_dir)
@@ -280,9 +287,7 @@ def _extract_file(self, fname, extract_dir):
                     subdir_members = [
                         info
                         for info in tar_file.getmembers()
-                        if os.path.normpath(info.name).startswith(
-                            os.path.normpath(member)
-                        )
+                        if _is_selected_member(info.name, member)
                     ]
                     # Extract the data file from within the archive
                     tar_file.extractall(
diff --git a/pooch/tests/test_archive_member_boundaries.py b/pooch/tests/test_archive_member_boundaries.py
new file mode 100644
index 00000000..78b3177d
--- /dev/null
+++ b/pooch/tests/test_archive_member_boundaries.py
@@ -0,0 +1,114 @@
+# Copyright (c) 2018 The Pooch Developers.
+# Distributed under the terms of the BSD 3-Clause License.
+# SPDX-License-Identifier: BSD-3-Clause
+#
+# This code is part of the Fatiando a Terra project (https://www.fatiando.org)
+#
+
+"""Regression tests for archive member selection boundaries."""
+
+from io import BytesIO
+from pathlib import Path
+from tarfile import TarFile, TarInfo
+from zipfile import ZipFile
+
+import pytest
+
+from ..processors import Untar, Unzip
+
+FILES = {
+    "selected/ok.txt": b"ok",
+    "selected/nested/a.txt": b"nested",
+    "selected/ok.txt.bak": b"backup",
+    "selected-extra/unexpected.txt": b"unexpected",
+    "selectedfile.txt": b"unexpected",
+    "other/keep.txt": b"other",
+}
+
+SELECTED = {
+    "selected/ok.txt",
+    "selected/nested/a.txt",
+    "selected/ok.txt.bak",
+}
+
+
+def make_archive(path):
+    """Create a small ZIP or TAR archive locally."""
+    if path.suffix == ".zip":
+        with ZipFile(path, "w") as archive:
+            for name, data in FILES.items():
+                archive.writestr(name, data)
+    else:
+        with TarFile.open(path, "w") as archive:
+            for name, data in FILES.items():
+                info = TarInfo(name)
+                info.size = len(data)
+                archive.addfile(info, BytesIO(data))
+
+
+@pytest.mark.parametrize(
+    ("processor_class", "extension"),
+    [(Unzip, ".zip"), (Untar, ".tar")],
+    ids=["zip", "tar"],
+)
+@pytest.mark.parametrize(
+    ("members", "expected"),
+    [
+        (["selected"], SELECTED),
+        (["selected/"], SELECTED),
+        (["./selected"], SELECTED),
+        (["selected/nested"], {"selected/nested/a.txt"}),
+        (["selected/ok.txt"], {"selected/ok.txt"}),
+        (["selectedfile.txt"], {"selectedfile.txt"}),
+        (
+            ["selected/ok.txt", "other/keep.txt"],
+            {"selected/ok.txt", "other/keep.txt"},
+        ),
+        (["missing"], set()),
+        (None, set(FILES)),
+    ],
+)
+def test_member_selection_boundaries(
+    tmp_path, processor_class, extension, members, expected
+):
+    """Only the requested members should be extracted and returned."""
+    archive = tmp_path / f"sample{extension}"
+    make_archive(archive)
+
+    processor = processor_class(members=members)
+    returned = processor(str(archive), "download", None)
+    output = Path(str(archive) + processor.suffix)
+
+    actual = {
+        path.relative_to(output).as_posix()
+        for path in output.rglob("*")
+        if path.is_file()
+    }
+    returned_paths = {Path(path).relative_to(output).as_posix() for path in returned}
+
+    assert actual == expected
+    assert returned_paths == expected
+
+
+@pytest.mark.parametrize(
+    ("processor_class", "extension"),
+    [(Unzip, ".zip"), (Untar, ".tar")],
+    ids=["zip", "tar"],
+)
+def test_existing_extraction_filters_returned_files(
+    tmp_path, processor_class, extension
+):
+    """Existing files with similar prefixes must not be returned."""
+    archive = tmp_path / f"sample{extension}"
+    make_archive(archive)
+
+    processor_class()(str(archive), "download", None)
+
+    processor = processor_class(members=["selected/ok.txt"])
+    returned = processor(str(archive), "fetch", None)
+    output = Path(str(archive) + processor.suffix)
+
+    returned_paths = {Path(path).relative_to(output).as_posix() for path in returned}
+
+    assert returned_paths == {"selected/ok.txt"}
+    assert (output / "selected/ok.txt.bak").exists()