diff --git a/strategy/cli.py b/strategy/cli.py
index a7139d7..0e30549 100644
--- a/strategy/cli.py
+++ b/strategy/cli.py
@@ -36,8 +36,8 @@ def build_parser() -> argparse.ArgumentParser:
                    help="test-matrix content. 'lowrank' = compressible data "
                         "where the strategy is accurate (default)")
     p.add_argument("--data-rank", type=int, default=None,
-                   help="rank of generated matrices when --fill lowrank "
-                        "(default n//32)")
+                   help="rank of generated matrices for --fill lowrank / "
+                        "decaying-spectrum (default max(1, n//32))")
     p.add_argument("--seed", type=int, default=0)
     p.add_argument("--verify", action="store_true",
                    help="report reconstruction error vs a float64 reference")
diff --git a/tests/test_data_rank_decaying_spectrum.py b/tests/test_data_rank_decaying_spectrum.py
new file mode 100644
index 0000000..0bd8d65
--- /dev/null
+++ b/tests/test_data_rank_decaying_spectrum.py
@@ -0,0 +1,37 @@
+"""`--data-rank` controls the rank of BOTH the lowrank and decaying-spectrum
+fills (storage.generate uses it for each), and its default is max(1, n//32) --
+not the bare n//32 the CLI help used to claim. These pure-NumPy checks pin that
+contract, backing the corrected --data-rank help text.
+"""
+from __future__ import annotations
+
+import numpy as np
+
+from strategy import storage
+
+
+def test_data_rank_sets_decaying_spectrum_rank():
+    for r in (2, 8, 20):
+        m = storage.generate(64, np.float64, False, None, seed=0,
+                              fill="decaying-spectrum", data_rank=r)
+        assert np.linalg.matrix_rank(m) == r
+
+
+def test_data_rank_sets_lowrank_rank():
+    for r in (3, 10):
+        m = storage.generate(64, np.float64, False, None, seed=0,
+                              fill="lowrank", data_rank=r)
+        assert np.linalg.matrix_rank(m) == r
+
+
+def test_default_data_rank_is_floored_at_one():
+    # n // 32 == 0 for small n, but the default is max(1, n//32), so a
+    # decaying-spectrum matrix is at least rank 1 (never rank 0 / all-zero).
+    m = storage.generate(16, np.float64, False, None, seed=0,
+                         fill="decaying-spectrum", data_rank=None)
+    assert np.linalg.matrix_rank(m) == 1
+
+
+if __name__ == "__main__":
+    import pytest
+    raise SystemExit(pytest.main([__file__, "-q"]))