diff --git a/news/tolerance.rst b/news/tolerance.rst
new file mode 100644
index 00000000..7d35607b
--- /dev/null
+++ b/news/tolerance.rst
@@ -0,0 +1,23 @@
+**Added:**
+
+* Option to set tolerance for the morph refinement (default 1e-08).
+
+**Changed:**
+
+* <news item>
+
+**Deprecated:**
+
+* <news item>
+
+**Removed:**
+
+* <news item>
+
+**Fixed:**
+
+* <news item>
+
+**Security:**
+
+* <news item>
diff --git a/src/diffpy/morph/morphapp.py b/src/diffpy/morph/morphapp.py
index ad7ca73c..3847bf9f 100755
--- a/src/diffpy/morph/morphapp.py
+++ b/src/diffpy/morph/morphapp.py
@@ -104,6 +104,13 @@ def custom_error(self, msg):
         type="float",
         help="Maximum r-value to use for PDF comparisons.",
     )
+    parser.add_option(
+        "--tolerance",
+        "-t",
+        type="float",
+        metavar="TOL",
+        help="Specify refiner tolerance as TOL. Default: 10e-8.",
+    )
     parser.add_option(
         "--pearson",
         action="store_true",
@@ -420,6 +427,11 @@ def single_morph(parser, opts, pargs, stdout_flag=True):
     if y_target is None:
         parser.error(f"No data table found in file: {pargs[1]}.")
 
+    # Get tolerance
+    tolerance = 1e-08
+    if opts.tolerance is not None:
+        tolerance = opts.tolerance
+
     # Get configuration values
     scale_in = "None"
     stretch_in = "None"
@@ -519,7 +531,9 @@ def single_morph(parser, opts, pargs, stdout_flag=True):
         refpars = list(set(refpars) - set(opts.exclude))
 
     # Refine or execute the morph
-    refiner = refine.Refiner(chain, x_morph, y_morph, x_target, y_target)
+    refiner = refine.Refiner(
+        chain, x_morph, y_morph, x_target, y_target, tolerance=tolerance
+    )
     if opts.pearson:
         refiner.residual = refiner._pearson
     if opts.addpearson:
diff --git a/src/diffpy/morph/refine.py b/src/diffpy/morph/refine.py
index 9514f8d8..c0c5eb60 100644
--- a/src/diffpy/morph/refine.py
+++ b/src/diffpy/morph/refine.py
@@ -42,12 +42,15 @@ class Refiner(object):
         to other functions.
     """
 
-    def __init__(self, chain, x_morph, y_morph, x_target, y_target):
+    def __init__(
+        self, chain, x_morph, y_morph, x_target, y_target, tolerance=1e-08
+    ):
         self.chain = chain
         self.x_morph = x_morph
         self.y_morph = y_morph
         self.x_target = x_target
         self.y_target = y_target
+        self.tolerance = tolerance
         self.pars = []
         self.residual = self._residual
         self.flat_to_grouped = {}
@@ -143,7 +146,11 @@ def refine(self, *args, **kw):
                 self.flat_to_grouped[len(initial) - 1] = (p, None)
 
         sol, cov_sol, infodict, emesg, ier = leastsq(
-            self.residual, initial, full_output=1
+            self.residual,
+            initial,
+            full_output=1,
+            ftol=self.tolerance,
+            xtol=self.tolerance,
         )
         fvec = infodict["fvec"]
 
diff --git a/tests/test_refine.py b/tests/test_refine.py
index 33d8d4ac..e7105a3e 100644
--- a/tests/test_refine.py
+++ b/tests/test_refine.py
@@ -46,7 +46,7 @@ def test_refine_morph(self, setup):
 
         assert (x_morph == x_target).all()
         assert numpy.allclose(y_morph, y_target)
-        pytest.approx(config["scale"], 3.0)
+        assert pytest.approx(config["scale"]) == 3.0
         return
 
     def test_refine_chain(self, setup):
@@ -74,8 +74,44 @@ def test_refine_chain(self, setup):
         err = 15.0 * 2
         res = sum(numpy.fabs(y_target - y_morph))
         assert res < err
-        pytest.approx(chain.scale, 3, 2)
-        pytest.approx(chain.stretch, 0.1, 2)
+        assert pytest.approx(chain.scale, 0.01, 0.01) == 3.0
+        assert pytest.approx(chain.stretch, 0.01, 0.01) == 0.1
+        return
+
+    def test_refine_tolerance(self, setup):
+        # Check that small tolerance gives good result
+        stol = 1e-16
+        config = {
+            "scale": 1.0,
+        }
+        mscale = MorphScale(config)
+        refiner = Refiner(
+            mscale,
+            self.x_morph,
+            self.y_morph,
+            self.x_target,
+            self.y_target,
+            tolerance=stol,
+        )
+        refiner.refine()
+        assert pytest.approx(config["scale"], stol, stol) == 3.0
+
+        # Check that larger tolerance does not give as good of result
+        ltol = 100
+        config = {
+            "scale": 1.0,
+        }
+        mscale = MorphScale(config)
+        refiner = Refiner(
+            mscale,
+            self.x_morph,
+            self.y_morph,
+            self.x_target,
+            self.y_target,
+            tolerance=ltol,
+        )
+        refiner.refine()
+        assert not pytest.approx(config["scale"], stol, stol) == 3.0
         return