diff --git a/news/enough-regression-points.rst b/news/enough-regression-points.rst
new file mode 100644
index 0000000..8ff9e7c
--- /dev/null
+++ b/news/enough-regression-points.rst
@@ -0,0 +1,23 @@
+**Added:**
+
+* Raise ``ValueError`` if the number of shared grid points between morphed and target functions is less than the number of parameters.
+
+**Changed:**
+
+* <news item>
+
+**Deprecated:**
+
+* <news item>
+
+**Removed:**
+
+* <news item>
+
+**Fixed:**
+
+* <news item>
+
+**Security:**
+
+* <news item>
diff --git a/src/diffpy/morph/refine.py b/src/diffpy/morph/refine.py
index 688e06e..8f1390d 100644
--- a/src/diffpy/morph/refine.py
+++ b/src/diffpy/morph/refine.py
@@ -83,7 +83,15 @@ def _residual(self, pvals):
             self.x_morph, self.y_morph, self.x_target, self.y_target
         )
         rvec = _y_target - _y_morph
-
+        if len(rvec) < len(pvals):
+            raise ValueError(
+                f"\nNumber of parameters (currently {len(pvals)}) cannot "
+                "exceed the number of shared grid points "
+                f"(currently {len(rvec)}). "
+                "Please reduce the number of morphing parameters or "
+                "provide new morphing and target functions with more "
+                "shared grid points."
+            )
         # If first time computing residual
         if self.res_length is None:
             self.res_length = len(rvec)
@@ -145,6 +153,9 @@ def refine(self, *args, **kw):
         ------
         ValueError
             Exception raised if a minimum cannot be found.
+        ValueError
+            If the number of shared grid points between morphed function and
+            target function is smaller than the number of parameters.
         """
 
         self.pars = args or self.chain.config.keys()
diff --git a/tests/test_refine.py b/tests/test_refine.py
index 4cf1bc7..76263bf 100644
--- a/tests/test_refine.py
+++ b/tests/test_refine.py
@@ -181,6 +181,62 @@ def stretch(x, y, stretch):
 
         assert res < err
 
+    def test_refine_grid_bad(self, user_filesystem):
+        grid = numpy.arange(2)
+        func = numpy.sin(grid)
+        grid1, func1, grid2, func2 = grid, func, grid, func
+        config = {
+            "stretch": 0.005,
+            "scale": 1.0,
+            "smear": 0,
+        }
+        chain = MorphChain(config)
+        refiner = Refiner(chain, grid1, func1, grid2, func2)
+        refpars = ["stretch", "scale", "smear"]
+        expected_error_message = (
+            "\nNumber of parameters (currently 3) cannot "
+            "exceed the number of shared grid points "
+            "(currently 2). "
+            "Please reduce the number of morphing parameters or "
+            "provide new morphing and target functions with more "
+            "shared grid points."
+        )
+        with pytest.raises(
+            ValueError,
+        ) as error:
+            refiner.refine(*refpars)
+        actual_error_message = str(error.value)
+        assert actual_error_message == expected_error_message
+
+        # call from command line
+        import subprocess
+
+        data_dir_path = user_filesystem / "cwd_dir"
+        morph_file = data_dir_path / "morph_data"
+        morph_data_text = [
+            str(grid1[i]) + " " + str(func1[i]) for i in range(len(grid1))
+        ]
+        morph_data_text = "\n".join(morph_data_text)
+        morph_file.write_text(morph_data_text)
+        target_file = data_dir_path / "target_data"
+        target_data_text = [
+            str(grid2[i]) + " " + str(func2[i]) for i in range(len(grid2))
+        ]
+        target_data_text = "\n".join(target_data_text)
+        target_file.write_text(target_data_text)
+        run_cmd = ["diffpy.morph"]
+        for key, value in config.items():
+            run_cmd.append(f"--{key}")
+            run_cmd.append(f"{value}")
+        run_cmd.extend([str(morph_file), str(target_file)])
+        run_cmd.append("-n")
+        result = subprocess.run(run_cmd, capture_output=True, text=True)
+        expected_error_message = (
+            "diffpy.morph: error: " + expected_error_message
+        )
+        actual_error_message = result.stderr.strip()
+        assert actual_error_message == expected_error_message
+
 
 # End of class TestRefine