diff --git a/ultraplot/axes/plot.py b/ultraplot/axes/plot.py
index ae387927f..612405a5c 100644
--- a/ultraplot/axes/plot.py
+++ b/ultraplot/axes/plot.py
@@ -4120,8 +4120,10 @@ def _parse_cmap(
         # Parse keyword args
         cmap_kw = cmap_kw or {}
         norm_kw = norm_kw or {}
-        # If norm is given we use it to set vmin and vmax
-        if (vmin is not None or vmax is not None) and norm is not None:
+        # If norm is an already-instantiated Normalize, extract vmin/vmax from it.
+        # When norm is a string or tuple it will be constructed later with the
+        # supplied vmin/vmax, so we must not reject them here.
+        if (vmin is not None or vmax is not None) and isinstance(norm, mcolors.Normalize):
             raise ValueError("If 'norm' is given, 'vmin' and 'vmax' must not be set.")
         if isinstance(norm, mcolors.Normalize):
             vmin = norm.vmin
diff --git a/ultraplot/tests/test_plot.py b/ultraplot/tests/test_plot.py
index 652f71856..7b3971232 100644
--- a/ultraplot/tests/test_plot.py
+++ b/ultraplot/tests/test_plot.py
@@ -612,6 +612,19 @@ def test_pie_labeled_series_in_dataframes():
     uplt.close(fig)
 
 
+def test_string_norm_with_vmin_vmax(rng):
+    """
+    When norm is a string (e.g. 'log'), vmin and vmax should be forwarded
+    to the normalizer constructor instead of raising ValueError.
+    Regression test for https://github.com/Ultraplot/UltraPlot/issues/689
+    """
+    data = 11 ** (0.25 * np.cumsum(rng.random((20, 20)), axis=0))
+    fig, ax = uplt.subplots()
+    m = ax.pcolormesh(data, cmap="magma", norm="log", vmin=1e-2)
+    assert m.norm.vmin == pytest.approx(1e-2)
+    uplt.close(fig)
+
+
 def test_color_parsing_for_none():
     """
     Ensure that none is not parsed to white