diff --git a/distributed/spill.py b/distributed/spill.py
index 7cba8161a7d..cbf03817a4b 100644
--- a/distributed/spill.py
+++ b/distributed/spill.py
@@ -14,7 +14,7 @@
 from distributed.sizeof import safe_sizeof
 
 logger = logging.getLogger(__name__)
-has_zict_210 = parse_version(zict.__version__) > parse_version("2.0.0")
+has_zict_210 = parse_version(zict.__version__) >= parse_version("2.1.0")
 
 
 class SpilledSize(NamedTuple):
@@ -63,7 +63,7 @@ def __init__(
     ):
 
         if max_spill is not False and not has_zict_210:
-            raise ValueError("zict > 2.0.0 required to set max_weight")
+            raise ValueError("zict >= 2.1.0 required to set max-spill")
 
         super().__init__(
             fast={},
diff --git a/distributed/tests/test_spill.py b/distributed/tests/test_spill.py
index c30aa6cefc6..55bbb6ad8ad 100644
--- a/distributed/tests/test_spill.py
+++ b/distributed/tests/test_spill.py
@@ -5,16 +5,18 @@
 
 import pytest
 
-zict = pytest.importorskip("zict")
-from packaging.version import parse as parse_version
-
 from dask.sizeof import sizeof
 
 from distributed.compatibility import WINDOWS
 from distributed.protocol import serialize_bytelist
-from distributed.spill import SpillBuffer
+from distributed.spill import SpillBuffer, has_zict_210
 from distributed.utils_test import captured_logger
 
+requires_zict_210 = pytest.mark.skipif(
+    not has_zict_210,
+    reason="requires zict version >= 2.1.0",
+)
+
 
 def psize(*objs) -> tuple[int, int]:
     return (
@@ -105,12 +107,6 @@ def test_spillbuffer(tmpdir):
     assert buf.slow.total_weight == psize(d, e)
 
 
-requires_zict_210 = pytest.mark.skipif(
-    parse_version(zict.__version__) <= parse_version("2.0.0"),
-    reason="requires zict version > 2.0.0",
-)
-
-
 @requires_zict_210
 def test_spillbuffer_maxlim(tmpdir):
     buf = SpillBuffer(str(tmpdir), target=200, max_spill=600, min_log_interval=0)