diff --git a/src/xopen/__init__.py b/src/xopen/__init__.py
index f401fbc..875b287 100644
--- a/src/xopen/__init__.py
+++ b/src/xopen/__init__.py
@@ -95,6 +95,7 @@
 
 class ProgramSettings(typing.NamedTuple):
     program_args: Tuple[str, ...]
+    acceptable_compression_levels: Tuple[int, ...] = tuple(range(1, 10))
     threads_flag: Optional[str] = None
     # This exit code is not interpreted as an error when terminating the process
     allowed_exit_code: Optional[int] = -signal.SIGTERM
@@ -106,14 +107,15 @@ class ProgramSettings(typing.NamedTuple):
 PROGRAM_SETTINGS: Dict[str, ProgramSettings] = {
     "pbzip2": ProgramSettings(
         ("pbzip2",),
+        tuple(range(1, 10)),
         "-p",
         allowed_exit_code=None,
         allowed_exit_message=b"\n *Control-C or similar caught [sig=15], quitting...",
     ),
-    "xz": ProgramSettings(("xz",), "-T"),
-    "zstd": ProgramSettings(("zstd",), "-T"),
-    "pigz": ProgramSettings(("pigz", "--no-name"), "-p"),
-    "gzip": ProgramSettings(("gzip", "--no-name")),
+    "xz": ProgramSettings(("xz",), tuple(range(0, 10)), "-T"),
+    "zstd": ProgramSettings(("zstd",), tuple(range(1, 20)), "-T"),
+    "pigz": ProgramSettings(("pigz", "--no-name"), tuple(range(0, 10)) + (11,), "-p"),
+    "gzip": ProgramSettings(("gzip", "--no-name"), tuple(range(1, 10))),
 }
 
 
@@ -208,6 +210,13 @@ def __init__(  # noqa: C901
             raise ValueError(
                 f"Mode is '{mode}', but it must be 'r', 'rb', 'w', 'wb', 'a', or 'ab'"
             )
+        if (
+            compresslevel
+            and compresslevel not in program_settings.acceptable_compression_levels
+        ):
+            raise ValueError(
+                f"compresslevel must be in {program_settings.acceptable_compression_levels}."
+            )
         path = os.fspath(path)
         if isinstance(path, bytes) and sys.platform == "win32":
             path = path.decode()
diff --git a/tests/test_xopen.py b/tests/test_xopen.py
index a0e8fd2..0e3ee11 100644
--- a/tests/test_xopen.py
+++ b/tests/test_xopen.py
@@ -258,10 +258,10 @@ def test_filename_not_a_string():
 def test_invalid_compression_level(tmp_path):
     # Can be any kind of exception depending on backend, OSError, zlib.error,
     # zlib_ng.error, isal_zlib.error, ValueError (etc.)
-    with pytest.raises(Exception) as e:
+    with pytest.raises(ValueError) as e:
         with xopen(tmp_path / "out.gz", mode="w", compresslevel=17) as f:
             f.write("hello")  # pragma: no cover
-    assert "level" in e.value.args[0]
+    assert "compresslevel must be" in e.value.args[0]
 
 
 @pytest.mark.parametrize("ext", extensions)