diff --git a/src/cmap/_colormap.py b/src/cmap/_colormap.py
index 748742ddc..741c451ef 100644
--- a/src/cmap/_colormap.py
+++ b/src/cmap/_colormap.py
@@ -15,6 +15,7 @@
 from . import _external
 from ._catalog import Catalog
 from ._color import Color, ColorLike
+from ._parametrized_colormaps import get_parametrized_colormap_function
 
 if TYPE_CHECKING:
     from collections.abc import Iterator
@@ -92,6 +93,8 @@ class Colormap:
         - a `str` containing a recognized string colormap name (e.g. `"viridis"`,
           `"magma"`), optionally suffixed with `"_r"` to reverse the colormap
           (e.g. `"viridis"`, `"magma_r"`).
+        - a `str` containing a registered colormap function name (e.g. `"cubehelix"`),
+          used with the `cmap_kwargs` parameter to pass function arguments.
         - An iterable of [ColorLike](../../colors.md#colorlike-objects) values (any
           object that can be cast to a [`Color`][cmap.Color]), or "color-stop-like"
           tuples ( `(float, ColorLike)` where the first element is a scalar value
@@ -109,6 +112,12 @@ class Colormap:
           the matplotlib docs for more.
         - a `Callable` that takes an array of N values in the range [0, 1] and returns
           an (N, 4) array of RGBA values in the range [0, 1].
+    cmap_kwargs : dict[str, Any] | None
+        Keyword arguments to pass to a colormap function when `value` is a string
+        naming a registered function (e.g. `"cubehelix"`). For example:
+        `Colormap("cubehelix", cmap_kwargs={"start": 1.0, "rotation": -1.0})`.
+        If provided when `value` is not a registered function name, a `ValueError`
+        will be raised.
     name : str | None
         A name for the colormap. If None, will be set to the identifier or the string
         `"custom colormap"`.
@@ -226,10 +235,16 @@ def __init__(
         under: ColorLike | None = None,
         over: ColorLike | None = None,
         bad: ColorLike | None = None,
+        cmap_kwargs: dict[str, Any] | None = None,
     ) -> None:
         self.info: CatalogItem | None = None
 
-        if isinstance(value, str):
+        if isinstance(value, str) and cmap_kwargs is not None:
+            name = name or value
+            colormap_func = get_parametrized_colormap_function(name)
+            colormap_func = partial(colormap_func, **cmap_kwargs)
+            stops = _parse_colorstops(colormap_func)
+        elif isinstance(value, str):
             rev = value.endswith("_r")
             info = self.catalog()[value[:-2] if rev else value]
             name = name or f"{info.namespace}:{info.name}"
diff --git a/src/cmap/_parametrized_colormaps.py b/src/cmap/_parametrized_colormaps.py
new file mode 100644
index 000000000..eee825616
--- /dev/null
+++ b/src/cmap/_parametrized_colormaps.py
@@ -0,0 +1,42 @@
+"""Registry of parametrized colormap functions."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING, Callable
+
+from .data.cubehelix import cubehelix
+
+if TYPE_CHECKING:
+    from typing import Any
+
+    import numpy as np
+
+    LutCallable = Callable[[np.ndarray], np.ndarray]
+
+# Registry of colormap functions that accept parameters
+FUNCTION_REGISTRY: dict[str, Callable[..., Any]] = {
+    "cubehelix": cubehelix,
+}
+
+
+def get_parametrized_colormap_function(name: str) -> Callable[..., Any]:
+    """
+    Get a parametrized colormap function by name.
+
+    Args:
+        name: Name of the colormap function
+
+    Returns
+    -------
+        The colormap function
+
+    Raises
+    ------
+        ValueError: If the function name is not in the registry
+    """
+    if name not in FUNCTION_REGISTRY:
+        available = ", ".join(sorted(FUNCTION_REGISTRY.keys()))
+        raise ValueError(
+            f"Unknown colormap function: {name!r}. Available functions: {available}"
+        )
+    return FUNCTION_REGISTRY[name]
diff --git a/tests/test_colormap.py b/tests/test_colormap.py
index 3a9484d71..bd63c428a 100644
--- a/tests/test_colormap.py
+++ b/tests/test_colormap.py
@@ -236,3 +236,18 @@ def test_shifted() -> None:
     assert cm.shifted(0.5).shifted(-0.5) == cm
     # two shifts of 0.5 should give the original array
     assert cm.shifted().shifted() == cm
+
+
+def test_function_colormap_with_cmap_kwargs() -> None:
+    # construct cubehelix with custom parameters
+    ch = Colormap("cubehelix", cmap_kwargs={"start": 1.0, "rotation": -1.0})
+
+    # values should be different from default cubehelix
+    default_ch = Colormap("cubehelix")
+    assert ch(0.5) != default_ch(0.5)
+
+
+def test_invalid_function_colormap_with_cmap_kwargs() -> None:
+    # name which doesn't map to a registered function should raise ValueError
+    with pytest.raises(ValueError, match="Unknown colormap function"):
+        Colormap("nonexistent_function", cmap_kwargs={"param": 1.0})